JEE Main 2023 — Electromagnetism

An electron is allowed to move with constant velocity along the axis of current carrying straight solenoid. (A) The electron will experience magnetic force along the axis of the solenoid. (B) The electron will not experience magnetic force. (C) The electron will continue to move along the axis of the solenoid. (D) The electron will be accelerated along the axis of the solenoid. (E) The electron will follow parabolic path-inside the solenoid. Choose the correct answer from the option given below:

If $\vec{E}$ and $\vec{K}$ represent electric field and propagation vectors of the EM waves in vacuum, then magnetic field vector is given by: ($\omega -$ angular frequency)

The magnetic field at the center of a circular coil of radius R carrying current I is

A charge particle moving in magnetic field $B,$ has the components of velocity along $B$ as well as perpendicular to $B$. The path of the charge particle will be

Two identical circular wires of radius $20\mathrm{cm}$ and carrying current $\sqrt{2}A$ are placed in perpendicular planes as shown in figure. The net magnetic field at the centre of the circular wires is$________\times {10}^{-8}T.$  (Take $\pi =3.14$)

A proton with a kinetic energy of $2.0\mathrm{eV}$ moves into a region of uniform magnetic field of magnitude $\frac{\pi }{2}\times {10}^{-3}T$. The angle between the direction of magnetic field and velocity of proton is ${60}^{o}$. The pitch of the helical path taken by the proton is ____ $\mathrm{cm}$. (Take, mass of proton $=1.6\times {10}^{-27}\mathrm{kg}$ and charge on proton $=1.6\times {10}^{-19}C$).

As shown in the figure, a long straight conductor with semicircular arc of radius $\frac{\pi }{10}m$ is carrying current $I=3A$. The magnitude of the magnetic field. at the center $O$ of the arc is: (The permeability of the vacuum $=4\pi \times {10}^{-7}{\mathrm{NA}}^{-2}$ ) 

A charge particle of $2\mu C$ accelerated by a potential difference of $100V$ enters a region of uniform magnetic field of magnitude $4\mathrm{mT}$ at right angle to the direction of field. The charge particle completes semicircle of radius $3\mathrm{cm}$ inside magnetic field. The mass of the charge particle is ______ $\times {10}^{-18}\mathrm{kg}$.

A long conducting wire having a current $I$ flowing through it, is bent into a circular coil of $N$ turns. Then it is bent into a circular coil of $n$ turns. The magnetic field is calculated at the centre of coils in both the cases. The ratio of the magnetic field in first case to that of second case is:

A bar magnet with a magnetic moment $5.0A{m}^{2}$ is placed in parallel position relative to a magnetic field of $0.4T$. The amount of required work done in turning the magnet form parallel to antiparallel position relative to the field direction is ________.

The magnetic moments associated with two closely wound circular coils $A$ and $B$ of radius ${r}_{A}=10\mathrm{cm}\text{and}{r}_{B}=20\mathrm{cm}$ respectively are equal if: (Where ${N}_{A},{I}_{A}\text{and}{N}_{B},{I}_{B}$ are number of turn and current of $A\text{and}B$ respectively)

As shown in the figure, a current of $2A$ flowing in an equilateral triangle of side $4\sqrt{3}\mathrm{cm}$ . The magnetic field at the centroid $O$ of the triangle is :  (Neglect the effect of earth’s magnetic field)

A square loop of area $25{\mathrm{cm}}^{2}$ has a resistance of $10\Omega$. The loop is placed in uniform magnetic field of magnitude $40.0T$. The plane of loop is perpendicular to the magnetic field. The work done in pulling the loop out of the magnetic field slowly and uniformly in $1.0$ sec, will be

For a moving coil galvanometer, the deflection in the coil is $0.05\mathrm{rad}$ when a current of $10\mathrm{mA}$ is passed through it. If the torsional constant of suspension wire is $4.0\times {10}^{–5}Nm{\mathrm{rad}}^{-1}$, the magnetic field is $0.01T$ and the number of turns in the coil is $200$, the area of each turn (in ${\mathrm{cm}}^{2}$ ) is :

A solenoid of $1200$ turns is wound uniformly in a single layer on a glass tube $2m$ long and $0.2m$ in diameter. The magnetic intensity at the center of the solenoid when a current of $2A$ flows through it is:

A long solenoid is formed by winding $70$ turns ${\mathrm{cm}}^{-1}$ . If $2.0A$ current flows, then the magnetic field produced inside the solenoid is ______________. $({\mu }_{0}=4\pi \times {10}^{–7}Tm{A}^{–1})$

A circular loop of radius $R$ is carrying current $iA$. The ratio of magnetic field at the centre of circular loop and at a distance $R$ from the center of the loop on its axis is :

Two long straight wires $P$ and $Q$ carrying equal current $10A$ each were kept parallel to each other at $5\mathrm{cm}$ distance. Magnitude of magnetic force experienced by $10\mathrm{cm}$ length of wire $P$ is ${F}_{1}$. If distance between wires is halved and currents on them are doubled, force ${F}_{2}$ on $10\mathrm{cm}$ length of wire $P$ will be:

As shown in the figure, a configuration of two equal point charges $({q}_{0}=+2\mu C)$ is placed on an inclined plane. Mass of each point charge is $20g$. Assume that there is no friction between charge and plane. For the system of two point charges to be in equilibrium (at rest) the height $h=x\times {10}^{-3}m$. The value of$x$ is $(\text{ Take }\frac{1}{4\pi {\epsilon }_{0}}=9\times {10}^{9}N{m}^{2}{C}^{-2},g=10m{s}^{-2})$ 

An insulated copper wire of $100$ turns is wrapped around a wooden cylindrical core of the cross-sectional area $24{\mathrm{cm}}^{2}$. The two ends of the wire are connected to a resistor. The total resistance in the circuit is $12\Omega$. If an externally applied uniform magnetic field in the core along its axis changes from $1.5T$ in one direction to $1.5T$ in the opposite direction, the charge flowing through a point in the circuit during the change of magnetic field will be _____ $\mathrm{mC}$.

In the given figure, an inductor and resistor are connected in series with a battery of $\mathrm{emf}$ $E$ volt. $\frac{{E}^{a}}{2b}J{s}^{-1}$ represents the maximum rate at which the energy is stored in the magnetic field (inductor). The numerical value of $\frac{b}{a}$ will be _____. 

A conducting circular loop is placed in a uniform magnetic field of $0.4T$ with its plane perpendicular to the field. Somehow, the radius of the loop starts expanding at a constant rate of $1\mathrm{mm}{s}^{-1}$. The magnitude of induced emf in the loop at an instant when the radius of the loop is $2\mathrm{cm}$ will be _______ $\mu V$.

The ratio of magnetic field at the centre of a current carrying coil of radius $r$ to the magnetic field at distance $r$ from the centre of coil on its axis is $\sqrt{x}:1$. The value of $x$ is _____.

A square shaped coil of area $70{\mathrm{cm}}^{2}$ having $600$ turns rotates in a magnetic field of $0.4\mathrm{Wb}{m}^{–2}$, about an axis which is parallel to one of the side of the coil and perpendicular to the direction of field. If the coil completes $500$ revolution in a minute, the instantaneous emf when the plane of the coil is inclined at $60^{\circ}$ with the field, will be ______ $V$. (Take $\pi =\frac{22}{7}$)

As per the given figure, if $\frac{dI}{dt}=-1A{s}^{-1}$, then the value of ${V}_{\mathrm{AB}}$ at this instant will be ______ $V$. 

Given below are two statements: Statement I : When the frequency of an AC source in a series LCR circuit increases, the current in the circuit first increases, attains a maximum value and then decreases. Statement II : In a series LCR circuit, the value of power factor at resonance is one. In the light of given statements, choose the most appropriate answer from the options given below.

Given below are two statements: Statement I: Maximum power is dissipated in a circuit containing an inductor, a capacitor and a resistor connected in series with an $AC$ source, when resonance occurs. Statement II: Maximum power is dissipated in a circuit containing pure resistor due to zero phase difference between current and voltage. In the light of the above statements, choose the correct answer from the options given below:

 As per the given graph, choose the correct representation for curve $A$ and curve $B$ {Where ${X}_{C}=$ Reactance of pure capacitive circuit connected with A.C. source ${X}_{L}=$ Reactance of pure inductive circuit connected with A.C. source $R=$ Impedance of pure resistive circuit connected with A.C. source $Z=$ Impedance of the $LCR$ series circuit }

A series LCR circuit is connected to an ac source of $220V,50\mathrm{Hz}$. The circuit contain a resistance $R=100\Omega$ and an inductor of inductive reactance ${X}_{L}=79.6\Omega$. The capacitance of the capacitor needed to maximize the average rate at which energy is supplied will be ______ $\mu F$.

Match the List-I with List-II. <table class="pyq-table"><tbody><tr><td></td><td>List I</td><td></td><td>List II</td></tr><tr><td>A</td><td>AC generator</td><td>I</td><td>Presence of both L and C</td></tr><tr><td>B</td><td>Transformer</td><td>II</td><td>Electromagnetic Induction</td></tr><tr><td>C</td><td>Resonance phenomenon to occur</td><td>III</td><td>Quality factor</td></tr><tr><td>D</td><td>Sharpness of resonance</td><td>IV</td><td>Mutual Inductance</td></tr></tbody></table>Choose the correct answer from the options given below:

An alternating voltage source $V=260\mathrm{sin}(628t)$ is connected across a pure inductor of $5\mathrm{mH}$. Inductive reactance in the circuit is:

In a series $LR$ circuit with ${X}_{L}=R$, power factor is ${P}_{1}$. If a capacitor of capacitance $C$ with ${X}_{C}={X}_{L}$ is added to the circuit the power factor becomes ${P}_{2}$. The ratio of ${P}_{1}$ to ${P}_{2}$ will be :

Three identical resistors with resistance $R=12\Omega$ and two identical inductors with sell inductance $L=5\mathrm{mH}$ are connected to an ideal battery with emf of $12V$ as shown in figure. The current through the battery long after the switch has been closed will be________$A$. 

A series LCR circuit is connected to an AC source of $220V$, $50\mathrm{Hz}$. The circuit contains a resistance $R=80\Omega$, an inductor of inductive reactance ${X}_{L}=70\Omega$, and a capacitor of capacitive reactance ${X}_{C}=130\Omega$. The power factor of circuit is $\frac{x}{10}$. The value of $x$ is:

For the given figures, choose the correct options: 

Match List-I with List II of Electromagnetic waves with corresponding wavelength range: <table class="pyq-table"><tbody><tr><td></td><td>List I</td><td></td><td>List II</td></tr><tr><td>(A)</td><td>Microwave</td><td>(I)</td><td>$400\mathrm{nm}$ to $1\mathrm{nm}$</td></tr><tr><td>(B)</td><td>Ultraviolet</td><td>(II)</td><td>$1\mathrm{nm}$ to ${10}^{–3}\mathrm{nm}$</td></tr><tr><td>(C)</td><td>$X$-Ray</td><td>(III)</td><td>$1\mathrm{mm}$ to $700\mathrm{nm}$</td></tr><tr><td>(D)</td><td>Infra-red</td><td>(IV)</td><td>$0.1m$ to $1\mathrm{mm}$</td></tr></tbody></table>Choose the correct answer from the options given below:

A plane electromagnetic wave of frequency $20\mathrm{MHz}$ propagates in free space along $x$-direction. At a particular space and time $\vec{E}=6.6\hat{j}V{m}^{-1}$. What is $\vec{B}$ at this point?

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A : EM waves used for optical communication have longer wavelengths than that of microwave, employed in Radar technology. Reason R : Infrared EM waves are more energetic than microwaves, (used in Radar) In the light of given statements, choose the correct answer from the options given below.

The energy density associated with electric field $\vec{E}$ and magnetic field $\vec{B}$ of an electromagnetic wave in free space is given by (${\epsilon }_{0}-$ permittivity of free space, ${\mu }_{0}-$ permeability of free space)

Match List I and List II <table class="pyq-table"><tbody><tr><td></td><td>List I</td><td></td><td>List II</td></tr><tr><td>A</td><td>Microwaves</td><td>I</td><td>Physiotherapy</td></tr><tr><td>B</td><td>UV rays</td><td>II</td><td>Treatment of cancer</td></tr><tr><td>C</td><td>Infra-red rays</td><td>III</td><td>Lasik eye surgery</td></tr><tr><td>D</td><td>X-rays</td><td>IV</td><td>Aircraft navigation</td></tr></tbody></table>Choose the correct answer from the option given below:

The electric field and magnetic field components of an electromagnetic wave going through vacuum is described by ${E}_{x}={E}_{0}\mathrm{sin}(kz-\omega t)$ ${B}_{y}={B}_{0}\mathrm{sin}(kz-\omega t)$ Then the correct relation between ${E}_{0}$ and ${B}_{0}$ is given by

All electromagnetic wave is transporting energy in the negative $z$ direction. At a certain point and certain time the direction of electric field of the wave is along positive $y$ direction. What will be the direction of the magnetic field of the wave at that point and instant?

Match List I and List II <table class="pyq-table"><tbody><tr><td>A</td><td>Gauss’s Law in Electrostatics</td><td>I</td><td>$\oint \vec{E}\cdot \vec{dl}=-\frac{d{\phi }_{B}}{dt}$</td></tr><tr><td>B</td><td>Faraday's Law</td><td>II</td><td>$\oint \vec{B}\cdot d\vec{A}=0$</td></tr><tr><td>C</td><td>Gauss’s Law in Magnetism</td><td>III</td><td>$\oint \vec{B}\cdot d\vec{l}={\mu }_{0}{i}_{c}+{\mu }_{0}{\in }_{0}\frac{d{\phi }_{E}}{dt}$</td></tr><tr><td>D</td><td>Ampere-Maxwell Law</td><td>IV</td><td>$\oint \vec{E}\cdot d\vec{s}=\frac{q}{{\in }_{0}}$</td></tr></tbody></table>Choose the correct answer from the options given below :

An oscillating $\mathrm{LC}$circuit consists of a $75\mathrm{mH}$ inductor and a $1.2\mu F$ capacitor. If the maximum charge to the capacitor is $2.7\mu C$. The maximum current in the circuit will be $_______\mathrm{mA}$.

Graphical variation of electric field due to a uniformly charged insulating solid sphere of radius $R,$with distance $r$ from the centre $O$ is represented by: 

A series LCR circuit consists of $R=80Ω$. ${X}_{L}=100Ω$, and ${X}_{C}=40Ω$. The input voltage is $2500\mathrm{cos}(100\pi t)V$. The amplitude of current, in the circuit, is _____ $A$.

The waves emitted when a metal target is bombarded with high energy electrons are

A $20\mathrm{cm}$ long metallic rod is rotated with $210\mathrm{rpm}$ about an axis normal to the rod passing through its one end. The other end of the rod is in contact with a circular metallic ring. A constant and uniform magnetic field $0.2T$ parallel to the axis exists everywhere. The emf developed between the centre and the ring is _________$\mathrm{mV}$. (Take $\pi =\frac{22}{7}$)

For the plane electromagnetic wave given by $E={E}_{0}\mathrm{sin}(\omega t–kx)$ and $B={B}_{0}\mathrm{sin}(\omega t-kx),$ the ratio of average electric energy density to average magnetic energy density is

As shown in the figure, a network of resistors is connected to a battery of $24V$ with an internal resistance of $3\Omega$. The currents through the resistors ${R}_{4}$ and ${R}_{5}$ are ${I}_{4}$ and ${I}_{5}$ respectively. The values of ${I}_{4}$ and ${I}_{5}$ are: 

A $1m$ long metal rod $XY$ completes the circuit as shown in figure. The plane of the circuit is perpendicular to the magnetic field of flux density $0.15T$. If the resistance of the circuit is $5Ω$, the force needed to move the rod in direction, as indicated, with a constant speed of $4m{s}^{-1}$ will be _______${10}^{–3}N$. 

An ideal transformer with purely resistive load operates at $12\mathrm{kV}$ on the primary side. It supplies electrical energy to a number of nearby houses at $120V.$ The average rate of energy consumption in the houses served by the transformer is $60\mathrm{kW}.$ The value of resistive load $({R}_{s})$ required in the secondary circuit will be$_________m\Omega .$

A single turn current loop in the shape of a right angle triangle with sides $5\mathrm{cm},12\mathrm{cm},13\mathrm{cm}$ is carrying a current of $2A$. The loop is in a uniform magnetic field of magnitude $0.75T$ whose direction is parallel to the current in the $13\mathrm{cm}$ side of the loop. The magnitude of the magnetic force on the $5\mathrm{cm}$ side will be $\frac{x}{130}N$. The value of $x$ is _______.

A certain elastic conducting material is stretched into a circular loop. It is placed with its plane perpendicular to a uniform magnetic field $B=0.8T$. When released the radius of the loop starts shrinking at a constant rate of $2\mathrm{cm}{s}^{–1}$. The induced emf in the loop at an instant when the radius of the loop is $10\mathrm{cm}$ will be ______ $\mathrm{mV}$.

Given below are two statements: Statement I: If the number of turns in the coil of a moving coil galvanometer is doubled then the current sensitivity becomes double. Statement II: Increasing current sensitivity of a moving coil galvanometer by only increasing the number of turns in the coil will also increase its voltage sensitivity in the same ratio In the light of the above statements, choose the correct answer from the options given below:

Two identical cells each of emf $1.5V$ are connected in series across a $10\Omega$ resistance. An ideal voltmeter connected across $10\Omega$ resistance reads $1.5V$. The internal resistance of each cell is _____ $\Omega$.

Find the mutual inductance in the arrangement, when a small circular loop of wire of radius $R$ is placed inside a large square loop of wire of side $L(L\gg R)$. The loops are coplanar and their centres coincide : 

A massless square loop, of wire of resistance $10\Omega$, supporting a mass of $1g$, hangs vertically with one of its sides in a uniform magnetic field of ${10}^{3}G$, directed outwards in the shaded region. A dc voltage $V$ is applied to the loop. For what value of $V$, the magnetic force will exactly balance the weight of the supporting mass of $1g$? (If sides of the loop $=10\mathrm{cm},g=10m{s}^{-2}$) .

In the network shown below, the charge accumulated in the capacitor in steady state will be: 

A parallel plate capacitor has plate area $40{\mathrm{cm}}^{2}$ and plates separation $2\mathrm{mm}$. The space between the plates is filled with a dielectric medium of a thickness $1\mathrm{mm}$ and dielectric constant $5$. The capacitance of the system is:

A straight wire carrying a current of $14A$ is bent into a semicircular arc of radius $2.2\mathrm{cm}$ as shown in the figure. The magnetic field produced by the current at the centre $O$ of the arc is ____ $\times {10}^{–4}T$ 

A square loop of side $2.0\mathrm{cm}$ is placed inside a long solenoid that has $50$ turns per centimetre and carries a sinusoidally varying current of amplitude $2.5A$ and angular frequency $700\mathrm{rad}{s}^{-1}$. The central axes of the loop and solenoid coincide. The amplitude of the emf induced in the loop is $x\times {10}^{-4}V$. The value of $x$ is ___________ $($ Take, $\pi =\frac{22}{7})$

A single current carrying loop of wire carrying current $I$ flowing in anticlockwise direction seen from $+vez$ direction and lying in $xy$ plane is shown in figure. The plot of $\hat{j}$ component of magnetic field $(By)$ at a distance $a$ (less than radius of the coil) and on $yz$ plane $vsz$ coordinate looks like 

In the given circuit, $rms$ value of current $({I}_{rms})$ through the resistor $R$ is : 

Let $\sigma$ be the uniform surface charge density of two infinite thin plane sheets shown in figure. Then the electric fields in three different region ${E}_{I},{E}_{II}$ and ${E}_{III}$ 

Find the magnetic field at the point P in figure. The curved portion is a semicircle connected to two long straight wires. 

Which of the following correctly represents the variation of electric potential $(V)$ of a charged spherical conductor of radius $(R)$ with radial distance $(r)$ from the centre?

Given below are two statements: Statement I : Out of microwaves, infrared rays and ultraviolet rays, ultraviolet rays are the most effective for the emission of electrons from a metallic surface Statement II : Above the threshold frequency, the maximum kinetic energy of photoelectrons is inversely proportional to the frequency of the incident light In the light of above statements, choose the correct answer from the options given below

A cubical volume is bounded by the surfaces $x=0,x=a,y=0,y=a,z=0,z=a$. The electric field in the region is given by $\vec{E}={E}_{0}x\hat{i}$. Where ${E}_{0}=4\times {10}^{4}{\mathrm{NC}}^{-1}{m}^{-1}$. If $a=2\mathrm{cm}$, the charge contained in the cubical volume is $Q\times {10}^{–14}C$. The value of $Q$ is ______. (Take ${\epsilon }_{0}=9\times {10}^{-12}{C}^{2}{N}^{-1}{m}^{-2}$)

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A : If an electric dipole of dipole moment $30\times {10}^{–5}Cm$ is enclosed by a closed surface, the net flux coming out of the surface will be zero. Reason R : Electric dipole consists of two equal and opposite charges. In the light of above, statements, choose the correct answer from the options given below.

If $V$ is the gravitational potential due to sphere of uniform density on its surface, then its value at the centre of sphere will be:

Experimentally it is found that $12.8\mathrm{eV}$ energy is required to separate a hydrogen atom into a proton and an electron. So the orbital radius of the electron in a hydrogen atom is $\frac{9}{x}\times {10}^{-10}m$. The value of the $x$ is: _____. ($1\mathrm{eV}=1.6\times {10}^{-19}J,\frac{1}{4\pi {\epsilon }_{0}}=9\times {10}^{9}\frac{{\mathrm{Nm}}^{2}}{{C}^{2}}$ and electronic charge $=1.6\times {10}^{-19}C$)

A dipole comprises of two charged particles of identical magnitude $q$ and opposite in nature. The mass $m$ of the positive charged particle is half of the mass of the negative charged particle. The two charges are separated by a distance $l$ . If the dipole is placed in a uniform electric field $\vec{E}$; in such a way that dipole axis makes a very small angle with the electric field, $\vec{E}$. The angular frequency of the oscillations of the dipole when released is given by:

An emf of $0.08V$ is induced in a metal rod of length $10\mathrm{cm}$ held normal to a uniform magnetic field of $0.4T$, when move with a velocity of:

Two isolated metallic solid spheres of radii $R$ and $2R$ are charged such that both have same charge density $\sigma$ . The spheres are then connected by a thin conducting wire. If the new charge density of the bigger sphere is ${\sigma }^{'}$. The ratio $\frac{{\sigma }^{'}}{\sigma }$ is :

In the given circuit, the equivalent resistance between the terminal A and B is ____ $\Omega$ 

The electric current in a circular coil of four turns produces a magnetic induction $32T$ at its centre. The coil is unwound and is rewound into a circular coil of single turn, the magnetic induction at the centre of the coil by the same current will be :

Which of the following are true? A. Speed of light in vacuum is dependent on the direction of propagation. B. Speed of light in a medium is independent of the wavelength of light. C. The speed of light is independent of the motion of the source. D. The speed of light in a medium is independent of intensity. Choose the correct answer from the question given below :

The induced emf can be produced in a coil by A. moving the coil with uniform speed inside uniform magnetic field B. moving the coil with non uniform speed inside uniform magnetic field C. rotating the coil inside the uniform magnetic field D. changing the area of the coil inside the uniform magnetic field Choose the correct answer from the options given below:

A uniform metallic wire carries a current $2A$, when $3.4V$ battery is connected across it. The mass of uniform metallic wire is $8.92\times {10}^{-3}\mathrm{kg}$, density is $8.92\times {10}^{3}\mathrm{kg}{m}^{-3}$ and resistivity is $1.7\times {10}^{-8}\Omega -m$ The length of wire is :

The amplitude of magnetic field in an electromagnetic wave propagating along $y$-axis is $6.0\times {10}^{–7}T$. The maximum value of electric field in the electromagnetic wave is

In an ac generator, a rectangular coil of $100$ turns each having area $14\times {10}^{–2}{m}^{2}$ is rotated at $360\mathrm{rev}{\mathrm{min}}^{-1}$ about an axis perpendicular to a uniform magnetic field of magnitude $3.0T$. The maximum value of the emf produced will be ______ $V$. [Take $\pi =\frac{22}{7}$]

If two charges ${q}_{1}$and ${q}_{2}$ are separated with distance $d$ and placed in a medium of dielectric constant $k$. What will be the equivalent distance between charges in air for the same electrostatic force?

The electric field in an electromagnetic wave is given as $\vec{E}=20\mathrm{sin}\omega (t-\frac{x}{c})\vec{j}N{C}^{-1}$, where $\omega$ and $c$ are angular frequency and velocity of electromagnetic wave respectively. The energy contained in a volume of $5\times {10}^{-4}{m}^{3}$ will be (Given ${\epsilon }_{0}=8.85\times {10}^{-12}{C}^{2}{N}^{-1}{m}^{-2}$)

A $12V$ battery connected to a coil of resistance $6Ω$ through a switch, drives a constant current in the circuit. The switch is opened in $1\mathrm{ms}$. The emf induced across the coil is $20V$. The inductance of the coil is :

A capacitor has capacitance $5\mu F$ when its parallel plates are separated by air medium of thickness $d$. A slab of material of dielectric constant $1.5$ having area equal to that of plates but thickness $\frac{d}{2}$ is inserted between the plates. Capacitance of the capacitor in the presence of slab will be ______ $\mu F$.

Ratio of thermal energy released in two resistor $R$ and $3R$ connected in parallel in an electric circuit is :

The magnetic intensity at the centre of a long current carrying solenoid is found to be $1.6\times {10}^{3}A{m}^{-1}$. If the number of turns is $8$ per $\mathrm{cm}$, then the current flowing through the solenoid is $______A.$

Given below are two statements: Statement I : An AC circuit undergoes electrical resonance if it contains either a capacitor or an inductor. Statement II: An AC circuit containing a pure capacitor or a pure inductor consumes high power due to its non-zero power factor. In the light of above statements, choose the correct answer from the options given below:

Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R. Assertion A : For measuring the potential difference across a resistance of $600\Omega$, the voltmeter with resistance $1000\Omega$ will be preferred over voltmeter with resistance $4000\Omega$. Reason R : Voltmeter with higher resistance will draw smaller current than voltmeter with lower resistance. In the light of the above statements, choose the most appropriate answer from the options given below

A $10\mu C$ charge is divided into two parts and placed at $1\mathrm{cm}$ distance so that the repulsive force between them is maximum. The charges of the two parts are:

For designing a voltmeter of range $50V$ and an ammeter of range $10\mathrm{mA}$ using a galvanometer which has a coil of resistance $54Ω$ showing a full scale deflection for $1\mathrm{mA}$ as in figure.  (A) for voltmeter $R\approx 50kΩ$ (B) for ammeter $r\approx 0.2Ω$ (C) for ammeter $r\approx 6Ω$ (D) for voltmeter $R\approx 5kΩ$ (E) for voltmeter $R\approx 500Ω$ Choose the correct answer from the options given below:

A metallic cube of side $15\mathrm{cm}$ moving along $y$-axis at a uniform velocity of $2m{s}^{-1}$. In a region of uniform magnetic field of magnitude $0.5T$ directed along $z$- axis. In equilibrium the potential difference between the faces of higher and lower potential developed because of the motion through the field will be $\mathrm{mV}$. 

An inductor of $0.5\mathrm{mH}$, a capacitor of $20\mu F$ and resistance of $20\Omega$ are connected in series with a $220V$ ac source. If the current is in phase with the emf, the amplitude of current of the circuit is $\sqrt{x}A$. The value of $x$ is-

Which of the following Maxwell’s equation is valid for time varying conditions but not valid for static conditions:

Expression for an electric field is given by $\vec{E}=4000{x}^{2}\hat{i}V{m}^{-1}$. The electric flux through the cube of side $20\mathrm{cm}$ when placed in electric field (as shown in the figure) is ______ $V\mathrm{cm}$. 

In the following circuit, the magnitude of current ${I}_{1}$, is ______ $A$. 

A coil has an inductance of $2H$ and resistance of $4\Omega$. A $10V$ is applied across the coil. The energy stored in the magnetic field after the current has built up to its equilibrium value will be _____ $\times {10}^{-2}J$

An inductor of inductance $2\mu H$ is connected in series with a resistance, a variable capacitor and an AC source of frequency $7\mathrm{kHz}$. The value of capacitance for which maximum current is drawn into the circuit is $\frac{1}{x}F$, where the value of $x$ is ______. (Take $\pi =\frac{22}{7}$)

Match the List-I with List-II: <table class="pyq-table"><tbody><tr><td></td><td>List I</td><td></td><td>List II</td></tr><tr><td>A</td><td>Microwaves</td><td>I</td><td>Radioactive decay of the nucleus</td></tr><tr><td>B</td><td>Gamma rays</td><td>II</td><td>Rapid acceleration and deceleration of electron in aerials</td></tr><tr><td>C</td><td>Radio waves</td><td>III</td><td>Inner shell electrons</td></tr><tr><td>D</td><td>X-rays</td><td>IV</td><td>Klystron valve</td></tr></tbody></table>Choose the correct answer from the options given below:

An LCR series circuit of capacitance $62.5\mathrm{nF}$ and resistance of $50\Omega$, is connected to an A.C. source of frequency $2.0\mathrm{kHz}$. For maximum value of amplitude of current in circuit, the value of inductance is ____$\mathrm{mH}$.$(\text{Take}{\pi }^{2}=10)$

The ratio of average electric energy density and total average energy density of electromagnetic wave is:

The source of time varying magnetic field may be (A) a permanent magnet (B) an electric field changing linearly with time (C) direct current (D) a decelerating charge particle (E) an antenna fed with a digital signal Choose the correct answer from the options given below.

The magnitude of magnetic induction at mid-point $O$ due to current arrangement as shown in figure will be .

A wire of length $1m$ moving with velocity $8m{s}^{-1}$ at right angles to a magnetic field of $2T$. The magnitude of induced emf, between the ends of wire will be ___________.

In an LC oscillator, if values of inductance and capacitance become twice and eight times, respectively, then the resonant frequency of oscillator becomes $x$ times its initial resonant frequency ${\omega }_{0}$. The value of $x$ is:

Two concentric circular coils with radii $1\mathrm{cm}$ and $1000\mathrm{cm}$ and number of turns $10$ and $200$ respectively are placed coaxially with centers coinciding. The mutual inductance of this arrangement will be _____ $\times {10}^{–8}H$. (Take, ${\pi }^{2}=10$)

An electron in a hydrogen atom revolves around its nucleus with a speed of $6.76\times {10}^{6}m{s}^{–1}$ in an orbit of radius $0.52Å$. The magnetic field produced at the nucleus of the hydrogen atom is _______ $T$.

An electron is moving along the positive x-axis. If uniform magnetic field is applied parallel to the negative z-axis, then A.The electron will experience magnetic force along positive y-axis B.The electron will experience magnetic force along negative y-axis C.The electron will not experience any force in magnetic field D.The electron will continue to move along the positive x-axis E.The electron will move along circular path in magnetic field Choose the correct answer from the option given below:

A conducting loop of radius $\frac{10}{\sqrt{\pi }}\mathrm{cm}$ is placed perpendicular to a uniform magnetic field of $0.5T$. The magnetic field is decreased to zero in $0.5s$ at a steady rate. The induced emf in the circular loop at $0.25s$ is:

In an electromagnetic wave, at an instant and at a particular position, the electric field is along the negative z-axis and magnetic field is along the positive x-axis. Then the direction of propagation of electromagnetic wave is:

A network of four resistances is connected to $9V$ battery, as shown in figure. The magnitude of voltage difference between the points $A$ and $B$ is __________ $V$. 

The drift velocity of electrons for a conductor connected in an electrical circuit is ${V}_{d}$. The conductor is now replaced by another conductor with same material and same length but double the area of cross-section. The applied voltage remains same. The new drift velocity of electrons will be

A rod with circular cross-section area $2{\mathrm{cm}}^{2}$ and length $40\mathrm{cm}$ is wound uniformly with $400$ turns of an insulated wire. If a current of $0.4A$ flows in the wire windings, the total magnetic flux produced inside windings is $4\pi \times {10}^{-6}\mathrm{Wb}$. The relative permeability of the rod is (Given : Permeability of vacuum ${\mu }_{0}=4\pi \times {10}^{-7}N{A}^{-2}$)

In the given circuit, the current $I$ through the battery will be 

A bar magnet is released from rest along the axis of a very long vertical copper tube. After some time the magnet will

A parallel plate capacitor of capacitance $2F$ is charged to a potential $V$. The energy stored in the capacitor is ${E}_{1}$. The capacitor is now connected to another uncharged identical capacitor in parallel combination. The energy stored in the combination is ${E}_{2}$. The ratio $\frac{{E}_{2}}{{E}_{1}}$ is

In the circuit shown, the energy stored in the capacitor is $n\mu J$. The value of $n$ is _____. 

A long straight wire of circular cross-section (radius $a$) is carrying steady current $I.$ The current $I$ is uniformly distributed across this cross-section. The magnetic field is

The equivalent resistance between $A$ and $B$ as shown in figure is: 

Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R. Assertion A : Two metallic spheres are charged to the same potential. One of them is hollow and another is solid, and both have the same radii. Solid sphere will have lower charge than the hollow one. Reason R : Capacitance of metallic spheres depend on the radii of spheres. In the light of the above statements, choose the correct answer from the options given below.

Electric potential at a point $P$ due to a point charge of $5\times {10}^{-9}C$ is $50V$. The distance of $P$ from the point charge is: (Assume, $\frac{1}{4\pi {\epsilon }_{0}}=9\times {10}^{9}N{m}^{2}{C}^{-2}$)

As shown in the figure, two parallel plate capacitors having equal plate area of $200{\mathrm{cm}}^{2}$ are joined in such a way that $a\neq b$. The equivalent capacitance of the combination is $x{\epsilon }_{0}F$. The value of $x$ is _____. 

Two long parallel wires carrying currents $8A$ and $15A$ in opposite directions are placed at a distance of $7\mathrm{cm}$ from each other. A point $P$ is at equidistant from both the wires such that the lines joining the point $P$ to the wires are perpendicular to each other. The magnitude of magnetic field at $P$ is ______ $\times {10}^{-6}T$. (Given: $\sqrt{2}=1.4$)

A point charge ${q}_{1}=4{q}_{0}$ is placed at origin. Another point charge ${q}_{2}=-{q}_{0}$ is placed at $x=12\mathrm{cm}$. Charge of proton is ${q}_{0}$. The proton is placed on $x$-axis so that the electrostatic force on the proton in zero. In this situation, the position of the proton from the origin is ______ $\mathrm{cm}$.

Match List I with List II <table class="pyq-table"><tbody><tr><td colspan="2" rowspan="1">List – I (Current configuration)</td><td colspan="2" rowspan="1">List – II (Magnetic field at point $O$)</td></tr><tr><td>A</td><td><img src="https://prepforbharat.s3.ap-south-1.amazonaws.com/exam/615f0e999476412f48314daf/Physics/images/Magnetic_Effects_of_Current/648b5a6f417cc3fb48d68059/question_1__q_648b5a6f417cc3fb48d68059__cdn-question-pool.getmarks.app__6d4d8a8b-2cf2-4134-983a-f4d799603481-30c03559-a817-48e9-903a__ea5c80dc0b_final_ppt_sync.png" alt="JEE Main 2023 Physics, Magnetic Effects of Current — question figure 1"></td><td>I.</td><td>${B}_{0}=\frac{{\mu }_{0}I}{4\pi r}[\pi +2]$</td></tr><tr><td>B</td><td><img src="https://prepforbharat.s3.ap-south-1.amazonaws.com/exam/615f0e999476412f48314daf/Physics/images/Magnetic_Effects_of_Current/648b5a6f417cc3fb48d68059/question_2__q_648b5a6f417cc3fb48d68059__cdn-question-pool.getmarks.app__fa41edbe-9bec-4bce-b977-38641dda9526-9894246_B__1d8500f970_final_ppt_sync.png" alt="JEE Main 2023 Physics, Magnetic Effects of Current — question figure 2"></td><td>II.</td><td>${B}_{0}=\frac{{\mu }_{0}}{4}\frac{I}{r}$</td></tr><tr><td>C</td><td><img src="https://prepforbharat.s3.ap-south-1.amazonaws.com/exam/615f0e999476412f48314daf/Physics/images/Magnetic_Effects_of_Current/648b5a6f417cc3fb48d68059/question_3__q_648b5a6f417cc3fb48d68059__cdn-question-pool.getmarks.app__0455c956-7478-44d1-aafb-f6da4de894cc-9894246_C__68b5fd56ef_final_ppt_sync.png" alt="JEE Main 2023 Physics, Magnetic Effects of Current — question figure 3"></td><td>III.</td><td>${B}_{0}=\frac{{\mu }_{0}I}{2\pi r}[\pi -1]$</td></tr><tr><td>D</td><td><img src="https://prepforbharat.s3.ap-south-1.amazonaws.com/exam/615f0e999476412f48314daf/Physics/images/Magnetic_Effects_of_Current/648b5a6f417cc3fb48d68059/question_4__q_648b5a6f417cc3fb48d68059__cdn-question-pool.getmarks.app__514b245c-d49c-45f0-bee9-5eeea479953f-9894246_D__0d22150df7_final_ppt_sync.png" alt="JEE Main 2023 Physics, Magnetic Effects of Current — question figure 4"></td><td>IV.</td><td>${B}_{0}=\frac{{\mu }_{0}I}{4\pi r}[\pi +1]$</td></tr></tbody></table>Choose the correct answer from the option given below:

A student is provided with a variable voltage source $V$, a test resistor ${R}_{T}=10\Omega$, two identical galvanometers ${G}_{1}$ and ${G}_{2}$ and two additional resistors, ${R}_{1}=10M\Omega$ and ${R}_{2}=0.001\Omega$. For conducting an experiment to verify ohm's law, the most suitable circuit is:

A coil is placed in magnetic field such that plane of coil is perpendicular to the direction of magnetic field. The magnetic flux through a coil can be changed: A. By changing the magnitude of the magnetic field within the coil. B. By changing the area of coil within the magnetic field. C. By changing the angle between the direction of magnetic field and the plane of the coil. D. By reversing the magnetic field direction abruptly without changing its magnitude. Choose the most appropriate answer from the options given below:

A current carrying circular loop of radius R produces a magnetic field B at its center. At what distance from center on its axis, the magnetic field becomes B/8?

Two identical heater filaments are connected first in parallel and then in series. At the same applied voltage, the ratio of heat produced in same time for parallel to series will be:

The $H$ amount of thermal energy is developed by a resistor in $10s$ when a current of $4A$ is passed through it. If the current is increased to $16A$, the thermal energy developed by the resistor in $10s$ will be

A metallic rod of length $L$ is rotated with an angular speed of $\omega$ normal to a uniform magnetic field $B$ about an axis passing through one end of rod as shown in figure. The induced emf will be : .

The energy of an electromagnetic wave contained in a small volume oscillates with

The magnetic field B crossing normally a square metallic plate of area $4{m}^{2}$ is changing with time as shown in figure. The magnitude of induced emf in the plate during $t=2s$ to $t=4s$, is _____ $mV$. 

A straight wire AB of mass $40g$ and length $50\mathrm{cm}$ is suspended by a pair of flexible leads in uniform magnetic field of magnitude $0.40T$ as shown in the figure. The magnitude of the current required in the wire to remove the tension in the supporting leads is _____ $A$. (Take $g=10m{s}^{-2})$. 

If a copper wire is stretched to increase its length by $20%$. The percentage increase in resistance of the wire is _____%.

A current carrying rectangular loop $PQRS$ is made of uniform wire. The length $PR=QS=5\mathrm{cm}\text{and}PQ=RS=100\mathrm{cm}$. If ammeter current reading changes from $I$ to $2I$, the ratio of magnetic forces per unit length on the wire $PQ$ due to wire $RS$ in the two cases respectively $({f}_{PQ}^{I}:{f}_{PQ}^{2I})$ is: 

The current sensitivity of moving coil galvanometer is increased by $25%$. This increase is achieved only changing in the number of turns of coils and area of cross section of the wire while keeping the resistance of galvanometer coil constant. The percentage change in the voltage sensitivity will be:

A capacitor of capacitance $150.0\mu F$ is connected to an alternating source of emf given by $E=36\mathrm{sin}(120\pi t)V$. The maximum value of current in the circuit is approximately equal to:

In this figure the resistance of the coil of galvanometer $G$ is $2Ω$. The emf of the cell is $4V$. The ratio of potential difference across ${C}_{1}$ and ${C}_{2}$ is 

The electric field at a distance r from an infinitely long uniformly charged wire having linear charge density λ is:

Given below are two statements : Statement I : Electromagnetic waves are not deflected by electric and magnetic field. Statement II : The amplitude of electric field and the magnetic field in electromagnetic waves are related to each other as ${E}_{0}=\sqrt{\frac{{\mu }_{0}}{{\epsilon }_{0}}}{B}_{0}$. In the light of the above statements, choose the correct answer from the options given below:

Two charges of each magnitude $0.01C$ and separated by a distance of $0.4\mathrm{mm}$ constitute an electric dipole. If the dipole is placed in an uniform electric field $\vec{E}$ of $10\mathrm{dyne}\cdot {C}^{-1}$ making ${30}^{\circ }$ angle with $\vec{E},$ the magnitude of torque acting on dipole is:

The electric field due to a short electric dipole at a large distance $(r)$ from center of dipole on the equatorial plane varies with distance as :

A thin infinite sheet charge and an infinite line charge of respective charge densities $+\sigma$ and $+\lambda$ are placed parallel at $5m$ distance from each other. Points $P$ and $Q$ are at $\frac{3}{\pi }m$ and $\frac{4}{\pi }m$ perpendicular distances from line charge towards sheet charge, respectively. ${E}_{p}$ and ${E}_{q}$ are the magnitudes of resultant electric field intensities at point $P$ and $Q$ respectively. If $\frac{{E}_{P}}{{E}_{Q}}=\frac{4}{a}$ for $2|\sigma |=|\lambda |,$ then the value of $a$ is _____.

Three point charges $q,-2q$ and $2q$ are placed on $x$ axis at a distance $x=0,x=\frac{3}{4}R$ and $x=R$ respectively from origin as shown. If $q=2\times {10}^{-6}C$ and $R=2\mathrm{cm}$, the magnitude of net force experienced by the charge $-2q$ is _____ $N$. 

Three concentric spherical metallic shells $X,Y$ and $Z$ of radius $a,b$ and $c$ respectively $[a<b<c]$ have surface charge densities $\sigma ,–\sigma$ and $\sigma$, respectively. The shells $X$ and $Z$ are at same potential. If the radii of $X&Y$ are $2\mathrm{cm}$ and $3\mathrm{cm}$, respectively. The radius of shell $Z$ is _____$\mathrm{cm}$.

An electron revolves around an infinite cylindrical wire having uniform linear charge density $2\times {10}^{-8}$ $C{m}^{-1}$ in circular path under the influence of attractive electrostatic field as shown in the figure. The velocity of electron with which it is revolving is ______________ $\times {10}^{6}m{s}^{-1}$. Given mass of electron $=9\times {10}^{-31}\mathrm{kg}$ 

An electric dipole of dipole moment is $6.0\times {10}^{-6}Cm$ placed in a uniform electric field of $1.5\times {10}^{3}N{C}^{-1}$ in such a way that dipole moment is along electric field. The work done in rotating dipole by $180^{\circ}$in this field will be_______$\mathrm{mJ}$.

Considering a group of positive charges, which of the following statements is correct?

Two equal positive point charges are separated by a distance $2a$. The distance of a point from the centre of the line joining two charges on the equatorial line (perpendicular bisector) at which force experienced by a test charge ${q}_{0}$ becomes maximum is $\frac{a}{\sqrt{x}}$. The value of $x$ is ______.

For a uniformly charged thin spherical shell, the electric potential $(V)$ radially away from the centre $(O)$ of shell can be graphically represented as 

As shown in figure, a cuboid lies in a region with electric field $E=2{x}^{2}\hat{i}-4y\hat{j}+6\hat{k}N{C}^{-1}$. The magnitude of charge within the cuboid is $n{\epsilon }_{0}C$. The value of $n$ is ______ (if dimension of cuboid is $1\times 2\times 3{m}^{3}$) 

As shown in the figure, a point charge $Q$ is placed at the centre of conducting spherical shell of inner radius $a$ and outer radius $b$. The electric field due to charge $Q$ in three different regions $I,II\text{and}III$ is given by : $(I:r<a,II:a<r<b,III:r>b)$ 

For a charged spherical ball, electrostatic potential inside the ball varies with $r$ as $V=2a{r}^{2}+b$. Here, $a$ and $b$ are constant and $r$ is the distance from the center. The volume charge density inside the ball is $-\lambda a\epsilon$. The value of $\lambda$ is ______. $\epsilon =$ permittivity of medium.

In a cuboid of dimension $2L\times 2L\times L$ , a charge $q$ is placed at the centre of the surface $S$ having area of $4{L}^{2}$ . The flux through the opposite surface to $S$ is given by

A point charge $2\times {10}^{–2}C$ is moved from $P$ to $S$ in a uniform electric field of $30N{C}^{–1}$ directed along positive $x$-axis. If coordinates of $P$ and $S$ are $(1,2,0)m\text{and}(0,0,0)m$ respectively, the work done by electric field will be

A stream of a positively charged particles having $\frac{q}{m}=2\times {10}^{11}C{\mathrm{kg}}^{-1}$ and velocity ${\vec{v}}_{0}=3\times {10}^{7}\hat{i}m{s}^{-1}$ is deflected by an electric field $1.8\hat{j}\mathrm{kV}{m}^{-1}$. The electric field exists in a region of $10\mathrm{cm}$ along $x$ direction. Due to the electric field, the deflection of the charge particles in the $y$ direction is _____ $\mathrm{mm}$.

The electric potential at the centre of two concentric half rings of radii ${R}_{1}$ and ${R}_{2}$, having same linear charge density $\lambda$ is .

A point charge of $10\mu C$ is placed at the origin. At what location on the $X$-axis should a point charge of $40\mu C$ be placed so that the net electric field is zero at $x=2\mathrm{cm}$ on the $X$-axis ?

A uniform electric field of $10N{C}^{-1}$ is created between two parallel charged plates (as shown in figure). An electron enters the field symmetrically between the plates with a kinetic energy $0.5\mathrm{eV}.$ The length of each plate is $10\mathrm{cm}$. The angle $(\theta )$ of deviation of the path of electron as it comes out of the field is ______(in degree). 

In the given figure the total charge stored in the combination of capacitors is $100\mu C$. The value of ‘$x$’ is ______________. 

A capacitor of capacitance $C$ is charged to a potential $V$. The flux of the electric field through a closed surface enclosing the positive plate of the capacitor is:

In the given circuit.${C}_{1}=2\mu F,{C}_{2}=0.2\mu F,{C}_{3}=2\mu F,{C}_{4}=4\mu F,{C}_{5}=$ $2\mu F,{C}_{6}=2\mu F$. The charge stored on capacitor ${C}_{4}$ is ______ $\mu C$. 

The equivalent capacitance of the combination shown is 

A $600\mathrm{pF}$ capacitor is charged by $200V$ supply. It is then disconnected from the supply and is connected to another uncharged $600\mathrm{pF}$ capacitor. Electrostatic energy lost in the process is _____ $\mu J$.

The distance between two plates of a capacitor is $d$ and its capacitance is ${C}_{1}$, when air is the medium between the plates. If a metal sheet of thickness $\frac{2d}{3}$ and of the same area as plate is introduced between the plates, the capacitance of the capacitor becomes ${C}_{2}$ . The ratio $\frac{{C}_{2}}{{C}_{1}}$ is

Two parallel plate capacitors ${C}_{1}$ and ${C}_{2}$ each having capacitance of $10\mu F$ are individually charged by a $100V$ D.C. source. Capacitor ${C}_{1}$ is kept connected to the source and a dielectric slab is inserted between it plates. Capacitor ${C}_{2}$ is disconnected from the source and then a dielectric slab is inserted in it. Afterwards the capacitor ${C}_{1}$ is also disconnected from the source and the two capacitors are finally connected in parallel combination. The common potential of the combination will be _____ $V$. (Assuming Dielectric constant $=10$)

A capacitor of capacitance $900\mu F$ is charged by a $100V$ battery. The capacitor is disconnected from the battery and connected to another uncharged identical capacitor such that one plate of uncharged capacitor connected to positive plate and another plate of uncharged capacitor connected to negative plate of the charged capacitor. The loss of energy in this process is measured as $x\times {10}^{-2}J$. The value of $x$ is ______.

A parallel plate capacitor with plate area $A$ and plate separation $d$ is filled with a dielectric material of dielectric constant $K=4.$ The thickness of the dielectric material is $x,$ where $x<d.$  Let ${C}_{1}$ and ${C}_{2}$ be the capacitance of the system for $x=\frac{1}{3}d$ and $x=\frac{2d}{3},$ respectively. If ${C}_{1}=2\mu F$, the value of ${C}_{2}$ is _____ $\mu F.$

A parallel plate capacitor with air between the plate has a capacitance of $15\mathrm{pF}$. The separation between the plate becomes twice and the space between them is filled with a medium of dielectric constant $3.5$. Then the capacitance becomes $\frac{x}{4}\mathrm{pF}$. The value of $x$ is____.

A current of $2A$ flows through a wire of cross-sectional area $25.0{\mathrm{mm}}^{2}$. The number of free electrons in a cubic meter are $2.0\times {10}^{28}$. The drift velocity of the electrons is _____ $\times {10}^{-6}{\mathrm{ms}}^{-1}$ (given, charge on electron $=1.6\times {10}^{-19}C$).

Equivalent resistance between the adjacent corners of a regular $n$-sided polygon of uniform wire of resistance $R$ would be :

When a resistance of $5\Omega$ is shunted with a moving coil galvanometer, it shows a full scale deflection for a current of $250\mathrm{mA},$ however when $1050\Omega$ resistance is connected with it in series, it gives full scale deflection for $25$ volt. The resistance of galvanometer is$_________\Omega .$

Different combination of $3$ resistors of equal resistance $R$ are shown in the figures. The increasing order for power dissipation is: (A)  (B)  (C)  (D) 

Given below are two statements: Statement I : The equivalent resistance of resistors in a series combination is smaller than least resistance used in the combination. Statement II : The resistivity of the material is independent of temperature. In the light of the above statements, choose the correct answer from the options given below:

A potential ${V}_{0}$ is applied across a uniform wire of resistance $R.$ The power dissipation is ${P}_{1}.$ The wire is then cut into two equal halves and a potential of ${V}_{0}$ is applied across the length of each half. The total power dissipation across two wires is ${P}_{2}.$ The ratio of ${P}_{2}:{P}_{1}$ is $\sqrt{x}:1.$ The value of $x$ is _____.

A wire of resistance $160Ω$ is melted and drawn in a wire of one-fourth of its length. The new resistance of the wire will be

The current flowing through a conductor connected across a source is $2A$ and $1.2A$ at ${0}^{o}C$ and ${100}^{o}C$ respectively. The current flowing through the conductor at ${50}^{o}C$ will be _____ $\times {10}^{2}\mathrm{mA}$.

 The current flowing through ${R}_{2}$ is :

In the circuit diagram shown in figure given below, the current flowing through resistance $3\Omega$ is $\frac{x}{3}A$. The value of $x$ is ________. 

A rectangular parallelopiped is measured as $1\mathrm{cm}\times 1\mathrm{cm}\times 100\mathrm{cm}$. If its specific resistance is $3\times {10}^{-7}\Omega m$, then the resistance between its two opposite rectangular faces will be _____$\times {10}^{-7}\Omega$. 

In a metallic conductor, under the effect of applied electric field, the free electrons of the conductor

$10$ resistors each of resistance $10Ω$ can be connected in such as to get maximum and minimum equivalent resistance. The ratio of maximum and minimum equivalent resistance will be________.

The number density of free electrons in copper is nearly $8\times {10}^{28}{m}^{-3}$. A copper wire has its area of cross-section $=2\times {10}^{-6}{m}^{2}$ and is carrying a current of $3.2A$. The drift speed of the electrons is _____$\times {10}^{-6}m{s}^{-1}$.

The equivalent resistance of the circuit shown below between points $a$ and $b$ is : 

Figure shows a part of an electric circuit. The potentials at points $a,b$ and $c$ are $30V,12V$ and $2V$ respectively. The current through the $20\Omega$ resistor will be, 

As shown in the figure the voltmeter reads $2V$ across $5\Omega$ resistor. The resistance of the voltmeter is _____ $\Omega$ 

In the given circuit the value of $|\frac{{I}_{1}+{I}_{3}}{{I}_{2}}|$ is: 

The equivalent resistance between $AandB$ of the network shown in figure: 

For the given circuit, in the steady state, $|{V}_{B}-{V}_{D}|=$ _____ $V$. 

Two identical cells, when connected either in parallel or in series gives same current in an external resistance $5\Omega$. The internal resistance of each cell will be ______ $\Omega$.

If the potential difference between $B$ and $D$ is zero, the value of $x$ is $\frac{1}{n}\Omega$. The value of $n$ is ______. 

The number of turns of the coil of a moving coil galvanometer is increased in order to increase current sensitivity by $50%$. The percentage change in voltage sensitivity of the galvanometer will be :

The charge flowing in a conductor changes with time as $Q(t)=\alpha t-\beta {t}^{2}+\gamma {t}^{3}$, where $\alpha ,\beta$ and $\gamma$ are constants. Minimum value of current is:

The equivalent resistance between $A\text{and}B$ is _______. .

The resistance of a wire is $5\Omega$. Its new resistance in ohm, if stretched to $5$ times of its original length will be :

Two cells are connected between points $A$ and $B$ as shown. Cell 1 has emf of $12V$ and internal resistance of $3\Omega$. Cell 2 has emf of $6V$ and internal resistance of $6\Omega$. An external resistor $R$ of $4\Omega$ is connected across $A$ and $B$. The current flowing through $R$ will be ______ $A$. 

A hollow cylindrical conductor has length of $3.14m$, while its inner and outer diameters are $4\mathrm{mm}$ and $8\mathrm{mm}$ respectively. The resistance of the conductor is $n\times {10}^{-3}\Omega$. If the resistivity of the material is $2.4\times {10}^{-8}\Omega m$. The value of $n$ is _____.

A cell of emf $90V$ is connected across series combination of two resistors each of $100\Omega$ resistance. A voltmeter of resistance $400\Omega$ is used to measure the potential difference across each resistor. The reading of the voltmeter will be:

Given below are two statements: Statement I: For diamagnetic substance $-1\leq x<0$, where $x$ is the magnetic susceptibility. Statement II: Diamagnetic substance when placed in an external magnetic field, tend to move from stronger to weaker part of the field. In the light of the above statements, choose the correct answer from the options give below.

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$ Assertion $A$: A bar magnet dropped through a metallic cylindrical pipe takes more time to come down compared to a non-magnetic bar with same geometry and mass. Reason $R$: For the magnetic bar, Eddy currents are produced in the metallic pipe which oppose the motion of the magnetic bar. In the light of the above statements, choose the correct answer from the options given below

Given below are two statements: Statement I : The diamagnetic property depends on temperature. Statement II : The induced magnetic dipole moment in a diamagnetic sample is always opposite to the magnetising field. In the light of given statements, choose the correct answer from the options given below

Given below are two statements: one is labelled as Assertion $A$ and the other is labelled as Reason $R$. Assertion A : Electromagnets are made of soft iron. Reason R : Soft iron has high permeability and low retentivity. In the light of above statements, choose the most appropriate answer from the options given below.

Certain galvanometers have a fixed core made of non magnetic metallic material. The function of this metallic material is

The current required to be passed through a solenoid of $15\mathrm{cm}$ length and $60$ turns in order to demagnetise a bar magnet of magnetic intensity $2.4\times {10}^{3}A{m}^{–1}$ is ________ $A$.