JEE Main 2024 — Electromagnetism

A 2 A current carrying straight metal wire of resistance $1 \Omega$, resistivity $2 \times 10^{-6} \Omega \mathrm{m}$, area of cross-section $10 \mathrm{~mm}^2$ and mass $500 \mathrm{~g}$ is suspended horizontally in mid air by applying a uniform magnetic field $\vec{B}$. The magnitude of $B$ is _____$\times 10^{-1} \mathrm{~T}$ (given, $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^2$ ).

A alternating current at any instant is given by $i=[6+\sqrt{56} \sin (100 \pi t+\pi / 3)]$ A. The $r m s$ value of the current is ________ A.

A bulb and a capacitor are connected in series across an ac supply. A dielectric is then placed between the plates of the capacitor. The glow of the bulb:

A capacitor has air as dielectric medium and two conducting plates of area $12 \mathrm{~cm}^2$ and they are $0.6 \mathrm{~cm}$ apart. When a slab of dielectric having area $12 \mathrm{~cm}^2$ and $0.6 \mathrm{~cm}$ thickness is inserted between the plates, one of the conducting plates has to be moved by $0.2 \mathrm{~cm}$ to keep the capacitance same as in previous case. The dielectric constant of the slab is : (Given $\epsilon_0=8.834 \times 10^{-12} \mathrm{~F} / \mathrm{m}$ )

A capacitor is made of a flat plate of area A and a second plate having a stair-like structure as shown in figure. If the area of each stair is $\frac{A}{3}$ and the height is $d$, the capacitance of the arrangement is : 

A capacitor of capacitance $C$ and potential $V$ has energy $E.$ It is connected to another capacitor of capacitance $2C$ and potential $2V$. Then the loss of energy is $\frac{x}{3}E$, where $x$ is _______.

A capacitor of capacitance $100\mu F$ is charged to a potential of $12V$ and connected to a $6.4\mathrm{mH}$ inductor to produce oscillations. The maximum current in the circuit would be :

A capacitor of $10 \mu \mathrm{F}$ capacitance whose plates are separated by $10 \mathrm{~mm}$ through air and each plate has area $4 \mathrm{~cm}^2$ is now filled equally with two dielectric media of $\mathrm{K}_1=2, \mathrm{~K}_2=3$ respectively as shown in figure. If new force between the plates is $8 \mathrm{~N}$. The supply voltage is _________ $\times 10^{-4} \mathrm{~V}$.  (we modified language of question to make it correct)

A capacitor of reactance $4 \sqrt{3} \Omega$ and a resistor of resistance $4 \Omega$ are connected in series with an ac source of peak value $8 \sqrt{2} \mathrm{~V}$. The power dissipation in the circuit is ________ W.

A charge $q$ is placed at the center of one of the surface of a cube. The flux linked with the cube is:

A charge of $4.0\mu C$ is moving with a velocity of $4.0\times {10}^{6}m{s}^{-1}$ along the positive $y$-axis under a magnetic field $B$ of strength $(2\hat{k})T$. The force acting on the charge is $x\hat{i}N$. The value of $x$ is ______.

A circular coil having 200 turns, $2.5 \times 10^{-4} \mathrm{~m}^2$ area and carrying $100 \mu \mathrm{A}$ current is placed in a uniform magnetic field of 1T. Initially the magnetic dipole moment $(\vec{M})$ was directed along $\vec{B}$. Amount of work, required to rotate the coil through $90^{\circ}$ from its initial orientation such that $\vec{M}$ becomes perpendicular to $\vec{B}$, is ______ $\mu \mathrm{J}$.

A coil having 100 turns, area of $5 \times 10^{-3} \mathrm{~m}^2$, carrying current of $1 \mathrm{~mA}$ is placed in uniform magnetic field of $0.20 \mathrm{~T}$ such a way that plane of coil is perpendicular to the magnetic field. The work done in turning the coil through $90^{\circ}$ is _______ $\mu \mathrm{J}$.

A coil is placed perpendicular to a magnetic field of $5000T$. When the field is changed to $3000T$ in $2s$, an induced emf of $22V$ is produced in the coil. If the diameter of the coil is $0.02m$, then the number of turns in the coil is:

A coil of negligible resistance is connected in series with $90 \Omega$ resistor across $120 \mathrm{~V}, 60 \mathrm{~Hz}$ supply. A voltmeter reads $36 \mathrm{~V}$ across resistance. Inductance of the coil is :

A coil of $200$ turns and area $0.20{m}^{2}$ is rotated at half a revolution per second and is placed in uniform magnetic field of $0.01T$ perpendicular to axis of rotation of the coil. The maximum voltage generated in the coil is $\frac{2\pi }{\beta }$ volt. The value of $\beta$ is ______.

A current of $200\mu A$ deflects the coil of a moving coil galvanometer through $60^{\circ}$. The current to cause deflection through $\frac{\pi }{10}$ radian is

A galvanmeter has a coil of resistance $200 \Omega$ with a full scale deflection at $20 \mu \mathrm{A}$. The value of resistance to be added to use it as an ammeter of range $(0-20) \mathrm{mA}$ is ;

A galvanometer has a resistance of $50\Omega$ and it allows maximum current of $5\mathrm{mA}$. It can be converted into voltmeter to measure upto $100V$ by connecting in series a resistor of resistance.

A galvanometer having coil resistance $10\Omega$ shows a full scale deflection for a current of $3\mathrm{mA}$. For it to measure a current of $8A$, the value of the shunt should be:

A galvanometer $(G)$ of $2\Omega$ resistance is connected in the given circuit. The ratio of charge stored in ${C}_{1}$ and ${C}_{2}$ is: 

A galvanometer of resistance $100 \Omega$ when connected in series with $400 \Omega$ measures a voltage of upto $10 \mathrm{~V}$. The value of resistance required to convert the galvanometer into ammeter to read upto $10 \mathrm{~A}$ is $x \times 10^{-2} \Omega$. The value of $x$ is :

A heater is designed to operate with a power of $1000 \mathrm{~W}$ in a $100 \mathrm{~V}$ line. It is connected in combination with a resistance of $10 \Omega$ and a resistance $R$, to a $100 \mathrm{~V}$ mains as shown in figure. For the heater to operate at $62.5 \mathrm{~W}$, the value of $\mathrm{R}$ should be _____$\Omega$. 

A horizontal straight wire $5m$ long extending from east to west falling freely at right angle to horizontal component of earth's magnetic field $0.60\times {10}^{-4}\mathrm{Wb}{m}^{-2}$. The instantaneous value of emf induced in the wire when its velocity is $10m{s}^{-1}$ is _______$\times {10}^{-3}V$.

A LCR circuit is at resonance for a capacitor $C$, inductance $L$ and resistance $R$. Now the value of resistance is halved keeping all other parameters same. The current amplitude at resonance will be now:

A long straight wire of radius a carries a steady current I. The current is uniformly distributed across its cross section. The ratio of the magnetic field at $\frac{a}{2}$ and $2 a$ from axis of the wire is :

A moving coil galvanometer has $100$ turns and each turn has an area of $2.0{\mathrm{cm}}^{2}.$ The magnetic field produced by the magnet is $0.01T$ and the deflection in the coil is $0.05$ radian when a current of $10\mathrm{mA}$ is passed through it. The torsional constant of the suspension wire is $x\times {10}^{-5}N-m/\mathrm{rad}.$ The value of $x$ is ______ .

A parallel plate capacitor has a capacitance $C=200\mathrm{pF}$. It is connected to $230V$ ac supply with an angular frequency $300\mathrm{rad}{s}^{-1}$. The rms value of conduction current in the circuit and displacement current in the capacitor respectively are :

A parallel plate capacitor of capacitance $12.5 \mathrm{pF}$ is charged by a battery connected between its plates to potential difference of $12.0 \mathrm{~V}$. The battery is now disconnected and a dielectric slab $\left(\epsilon_{\mathrm{r}}=6\right)$ is inserted between the plates. The change in its potential energy after inserting the dielectric slab is _____ $10^{-12} \mathrm{~J}$.

A parallel plate capacitor with plate separation $5\mathrm{mm}$ is charged up by a battery. It is found that on introducing a dielectric sheet of thickness $2\mathrm{mm}$, while keeping the battery connections intact, the capacitor draws $25%$ more charge from the battery than before. The dielectric constant of the sheet is ____.

A particle of charge $-q$ and mass $m$ moves in a circle of radius $r$ around an infinitely long line charge of linear density $+\lambda$. Then time period will be given as: (Consider $k$ as Coulomb's constant)

A plane electromagnetic wave of frequency $35\mathrm{MHz}$ travels in free space along the $X$-direction. At a particular point (in space and time) $\vec{E}=9.6\hat{j}V{m}^{-1}$. The value of magnetic field at this point is:

A plane electromagnetic wave propagating in $x$-direction is described by ${E}_{y}=(200V{m}^{-1})\mathrm{sin}[1.5\times {10}^{7}t-0.05x];$The intensity of the wave is : (Use ${\epsilon }_{0}=8.85\times {10}^{-12}{C}^{2}{N}^{-1}{m}^{-2}$)

A plane EM wave is propagating along $x$ direction. It has a wavelength of $4 \mathrm{~mm}$. If electric field is in $y$ direction with the maximum magnitude of $60 \mathrm{Vm}^{-1}$, the equation for magnetic field is :

A potential divider circuit is shown in figure. The output voltage ${V}_{0}$ is 

A power transmission line feeds input power at $2.3\mathrm{kV}$ to a step down transformer with its primary winding having $3000\text{turns}$. The output power is delivered at $230V$ by the transformer. The current in the primary of the transformer is $5A$ and its efficiency is $90%$. The winding of transformer is made of copper. The output current of transformer is ____$A$.

A proton and a deutron ( $q=+\mathrm{e}, m=2.0 \mathrm{u})$ having same kinetic energies enter a region of uniform magnetic field $\vec{B}$, moving perpendicular to $\vec{B}$. The ratio of the radius $r_d$ of deutron path to the radius $r_p$ of the proton path is:

A proton moving with a constant velocity passes through a region of space without any change in its velocity. If $\vec{E}$ and $\vec{B}$ represent the electric and magnetic fields respectively, then the region of space may have : (A) $E=0,B=0$; (B) $E=0,B\neq 0$; (C) $E\neq 0,B=0$; (D) $E\neq 0,B\neq 0$ Choose the most appropriate answer from the options given below :

A rectangular loop of length $2.5m$ and width $2m$ is placed at $60^{\circ}$ to a magnetic field of $4T$. The loop is removed from the field in $10\mathrm{sec}$. The average emf induced in the loop during this time is

A rectangular loop of sides $12\mathrm{cm}$ and $5\mathrm{cm}$, with its sides parallel to the $x$-axis and $y$-axis respectively moves with a velocity of $5\mathrm{cm}{s}^{-1}$ in the positive $x$ axis direction, in a space containing a variable magnetic field in the positive $z$ direction. The field has a gradient of ${10}^{-3}T{\mathrm{cm}}^{-1}$ along the negative $x$ direction and it is decreasing with time at the rate of ${10}^{-3}T{s}^{-1}.$ If the resistance of the loop is $6m\Omega$, the power dissipated by the loop as heat is ______ $\times {10}^{-9}W.$

A regular polygon of $6$ sides is formed by bending a wire of length $4\pi$ meter. If an electric current of $4\pi \sqrt{3}A$ is flowing through the sides of the polygon, the magnetic field at the centre of the polygon would be $x\times {10}^{-7}T.$ The value of $x$ is ______.

A rigid wire consists of a semicircular portion of radius $R$ and two straight sections. The wire is partially immerged in a perpendicular magnetic field $B={B}_{0}\hat{j}$ as shown in figure. The magnetic force on the wire if it has a current $i$ is : 

A rod of length $60 \mathrm{~cm}$ rotates with a uniform angular velocity $20 \mathrm{rad} \mathrm{s}^{-1}$ about its perpendicular bisector, in a uniform magnetic filed $0.5 T$. The direction of magnetic field is parallel to the axis of rotation. The potential difference between the two ends of the rod is _____V.

A series $LR$ circuit connected with an ac source $E=(25\mathrm{sin}1000t)V$ has a power factor of $\frac{1}{\sqrt{2}}$. If the source of emf is changed to $E=(20\mathrm{sin}2000t)V$, the new power factor of the circuit will be :

A series LCR circuit is subjected to an ac signal of $200 \mathrm{~V}, 50 \mathrm{~Hz}$. If the voltage across the inductor $(\mathrm{L}=10 \mathrm{mH})$ is $31.4 \mathrm{~V}$, then the current in this circuit is _____ .

A series LCR circuit with $L=\frac{100}{\pi }\mathrm{mH},C=\frac{{10}^{-3}}{\pi }F$ and $R=10\Omega$, is connected across an AC source of $220V,50\mathrm{Hz}$ supply. The power factor of the circuit would be ____.

A small square loop of wire of side $l$ is placed inside a large square loop of wire of side $L$$(L={l}^{2})$. The loops are coplanar and their centers coincide. The value of the mutual inductance of the system is $\sqrt{x}\times {10}^{-7}H$, where $x=$______.

A solenoid of length $0.5 \mathrm{~m}$ has a radius of $1 \mathrm{~cm}$ and is made up of ' $\mathrm{m}$ ' number of turns. It carries a current of $5 \mathrm{~A}$. If the magnitude of the magnetic field inside the solenoid is $6.28 \times 10^{-3} \mathrm{~T}$ then the value of $m$ is _____.

A square loop of edge length $2 \mathrm{~m}$ carrying current of $2 \mathrm{~A}$ is placed with its edges parallel to the $x$ $y$ axis. A magnetic field is passing through the $x-y$ plane and expressed as $\vec{B}=B_0(1+4 x) \hat{k}$, where $B_0=5 \mathrm{~T}$. The net magnetic force experienced by the loop is _______ $\mathrm{N}$.

A square loop of side $10\mathrm{cm}$ and resistance $0.7\Omega$ is placed vertically in the east-west plane. A uniform magnetic field of $0.20T$ is set up across the plane in the north-east direction. The magnetic field is decreased to zero in $1s$ at a steady rate. Then, the magnitude of induced emf is $\sqrt{x}\times {10}^{-3}V$. The value of $x$ is _______.

A square loop of side $15 \mathrm{~cm}$ being moved towards right at a constant speed of 2 $\mathrm{cm} / \mathrm{s}$ as shown in figure. The front edge enters the $50 \mathrm{~cm}$ wide magnetic field at $t=$ 0 . The value of induced emf in the loop at $t=10 \mathrm{~s}$ will be : 

A square loop PQRS having 10 turns, area $3.6 \times 10^{-3} \mathrm{~m}^2$ and resistance $100 \Omega$ is slowly and uniformly being pulled out of a uniform magnetic field of magnitude $\mathrm{B}=0.5 \mathrm{~T}$ as shown. Work done in pulling the loop out of the field in $1.0 \mathrm{~s}$ is ______ $\times 10^{-6} \mathrm{~J}$. 

A straight magnetic strip has a magnetic moment of $44 \mathrm{Am}^2$. If the strip is bent in a semicircular shape, its magnetic moment will be _______ $\mathrm{Am}^2$. (given $\pi=\frac{22}{7}$ )

A thin metallic wire having cross sectional area of ${10}^{-4}{m}^{2}$ is used to make a ring of radius $30\mathrm{cm}$. A positive charge of $2\pi C$ is uniformly distributed over the ring, while another positive charge of $30\mathrm{pC}$ is kept at the centre of the ring. The tension in the ring is $_______N$; provided that the ring does not get deformed (neglect the influence of gravity). (Given, $\frac{1}{4\pi {\epsilon }_{0}}=9\times {10}^{9}$ SI units)

A transformer has an efficiency of $80%$ and works at $10V$ and $4\mathrm{kW}.$ If the secondary voltage is $240V,$ then the current in the secondary coil is:

A uniform magnetic field of $2\times {10}^{-3}T$ acts along positive Y-direction. A rectangular loop of sides $20\mathrm{cm}$ and $10\mathrm{cm}$ with current of $5A$ is in Y-Z plane. The current is in anticlockwise sense with reference to negative X axis. Magnitude and direction of the torque is :

A $16\Omega$ wire is bend to form a square loop. A $9V$ battery with internal resistance $1\Omega$ is connected across one of its sides. If a $4\mu F$ capacitor is connected across one of its diagonals, the energy stored by the capacitor will be $\frac{x}{2}\mu J$, where $x=$______.

A wire of length $10\mathrm{cm}$ and radius $\sqrt{7}\times {10}^{-4}m$ connected across the right gap of a meter bridge. When a resistance of $4.5\Omega$ is connected on the left gap by using a resistance box, the balance length is found to be at $60\mathrm{cm}$ from the left end. If the resistivity of the wire is $R\times {10}^{-7}\Omega m$, then value of $R$ is :

A wire of resistance $R$ and length $L$ is cut into $5$ equal parts. If these parts are joined parallely, then resultant resistance will be :

A wire of resistance $R$ and radius $r$ is stretched till its radius became $r / 2$. If new resistance of the stretched wire is $x R$, then value of $x$ is _______

A wire of resistance $20 \Omega$ is divided into 10 equal parts, resulting pairs. A combination of two parts are connected in parallel and so on. Now resulting pairs of parallel combination are connected in series. The equivalent resistance of final combination is _____ $\Omega$.

An ac source is connected in given series LCR circuit. The rms potential difference across the capacitor of $20 \mu \mathrm{F}$ is _____V. 

An AC voltage $V=20\mathrm{sin}200\pi t$ is applied to a series LCR circuit which drives a current $I=10\mathrm{sin}(200\pi t+\frac{\pi }{3})$. The average power dissipated is:

An alternating emf $\mathrm{E}=110 \sqrt{2} \sin 100 \mathrm{t}$ volt is applied to a capacitor of $2 \mu \mathrm{F}$, the rms value of current in the circuit is _____$\mathrm{mA}$,

An alternating voltage of amplitude $40 \mathrm{~V}$ and frequency $4 \mathrm{kHz}$ is applied directly across the capacitor of $12 \mu \mathrm{F}$. The maximum displacement current between the plates of the capacitor is nearly :

An alternating voltage $V(t)=220\mathrm{sin}100\pi t$ volt is applied to a purely resistive load of $50\Omega$. The time taken for the current to rise from half of the peak value to the peak value is:

An electric bulb rated $50 \mathrm{~W}-200 \mathrm{~V}$ is connected across a $100 \mathrm{~V}$ supply. The power dissipation of the bulb is:

An electric charge ${10}^{-6}\mu C$ is placed at origin $(0,0)$ $m$ of $X-Y$ co-ordinate system. Two points $P$ and $Q$ are situated at $(\sqrt{3},\sqrt{3})m$ and $(\sqrt{6},0)m$ respectively. The potential difference between the points $P$ and $Q$ will be :

An electric field $\vec{E}=(2 x \hat{i}) N C^{-1}$ exists in space. A cube of side $2 \mathrm{~m}$ is placed in the space as per figure given below. The electric flux through the cube is ______ $\mathrm{Nm}^2 / \mathrm{C}$. 

An electric field is given by $(6\hat{i}+5\hat{j}+3\hat{k})N{C}^{-1}$. The electric flux through a surface area $30\hat{i}{m}^{2}$ lying in YZ-plane(in SI unit) is:

An electric field, $\overrightarrow{\mathrm{E}}=\frac{2 \hat{i}+6 \hat{j}+8 \hat{k}}{\sqrt{6}}$ passes through the surface of $4 \mathrm{~m}^2$ area having unit vector $\hat{n}=\left(\frac{2 \hat{i}+\hat{j}+\hat{k}}{\sqrt{6}}\right)$. The electric flux for that surface is ______ $\mathrm{Vm}$.

An electric toaster has resistance of $60\Omega$ at room temperature $(27^{\circ}C)$. The toaster is connected to a $220V$ supply. If the current flowing through it reaches $2.75A$, the temperature attained by toaster is around: (if $\alpha =2\times {10}^{-4}C-1\circ$ )

An electron is moving under the influence of the electric field of a uniformly charged infinite plane sheet $S$ having surface charge density $+\sigma$. The electron at $t=0$ is at a distance of $1m$ from $S$ and has a speed of $1m{s}^{-1}$. The maximum value of $\sigma$, if the electron strikes $S$ at $t=1s$ is $\alpha [\frac{m{\epsilon }_{0}}{e}]\frac{C}{{m}^{2}}$. The value of $\alpha$ is _____.

An electron is projected with uniform velocity along the axis inside a current carrying long solenoid. Then :

An electron moves through a uniform magnetic field $\vec{B}={B}_{0}\hat{i}+2{B}_{0}\hat{j}T$. At a particular instant of time, the velocity of electron is $\vec{u}=3\hat{i}+5\hat{j}m{s}^{-1}$. If the magnetic force acting on electron is $\vec{F}=5e\hat{k}N$, where $e$ is the charge of electron, then the value of ${B}_{0}$ is ____ $T$.

An electron with kinetic energy $5 \mathrm{eV}$ enters a region of uniform magnetic field of 3 $\mu \mathrm{T}$ perpendicular to its direction. An electric field $\mathrm{E}$ is applied perpendicular to the direction of velocity and magnetic field. The value of $E$, so that electron moves along the same path, is _______ $\mathrm{NC}^{-1}$. $\left(\right.$ Given, mass of electron $=9 \times 10^{-31} \mathrm{~kg}$, electric charge $\left.=1.6 \times 10^{-19} \mathrm{C}\right)$

An element $\Delta l=\Delta x \hat{i}$ is placed at the origin and carries a large current $I=10 \mathrm{~A}$. The magnetic field on the $y$-axis at a distance of $0.5 \mathrm{~m}$ from the elements $\Delta x$ of $1 \mathrm{~cm}$ length is: 

An infinite plane sheet of charge having uniform surface charge density $+\sigma_s \mathrm{C} / \mathrm{m}^2$ is placed on $x-y$ plane. Another infinitely long line charge having uniform linear charge density $+\lambda_e \mathrm{C} / \mathrm{m}$ is placed at $z=4 \mathrm{~m}$ plane and parallel to $y$-axis. If the magnitude values $\left|\sigma_{\mathrm{s}}\right|=2\left|\lambda_{\mathrm{e}}\right|$ then at point $(0,0,2)$, the ratio of magnitudes of electric field values due to sheet charge to that of line charge is $\pi \sqrt{n}: 1$. The value of $n$ is_______.

An infinitely long positively charged straight thread has a linear charge density $\lambda \mathrm{Cm}^{-1}$. An electron revolves along a circular path having axis along the length of the wire. The graph that correctly represents the variation of the kinetic energy of electron as a function of radius of circular path from the wire is :

An object is placed in a medium of refractive index $3$. An electromagnetic wave of intensity $6\times {10}^{8}W{m}^{-2}$ falls normally on the object and it is absorbed completely. The radiation pressure on the object would be (speed of light in free space $=3\times {10}^{8}m{s}^{-1}$ ):

${C}_{1}$ and ${C}_{2}$ are two hollow concentric cubes enclosing charges $2Q$ and $3Q$ respectively as shown in figure. The ratio of electric flux passing through ${C}_{1}$ and ${C}_{2}$ is: 

Arrange the following in the ascending order of wavelength: A. Gamma rays $\left(\lambda_1\right)$ B. $x$ - rays $\left(\lambda_2\right)$ C. Infrared waves $\left(\lambda_3\right)$ D. Microwaves $\left(\lambda_4\right)$ Choose the most appropriate answer from the options given below

At the centre of a half ring of radius $\mathrm{R}=10 \mathrm{~cm}$ and linear charge density $4 \mathrm{n} \mathrm{C} \mathrm{m}^{-1}$, the potential is $x \pi \mathrm{V}$. The value of $x$ is _______

By what percentage will the illumination of the lamp decrease if the current drops by $20%$?

Electromagnetic waves travel in a medium with speed of $1.5 \times 10^8 \mathrm{~m} \mathrm{~s}^{-1}$. The relative permeability of the medium is 2.0 . The relative permittivity will be:

Equivalent resistance of the following network is ________ $\Omega$. 

Five charges $+q,+5 q,-2 q,+3 q$ and $-4 q$ are situated as shown in the figure. The electric flux due to this configuration through the surface $S$ is : 

For a given series LCR circuit it is found that maximum current is drawn when value of variable capacitance is $25 \mathrm{nF}$. If resistance of $200 \Omega$ and $100 \mathrm{mH}$ inductor is being used in the given circuit. The frequency of ac source is ______ $\times 10^3 \mathrm{~Hz}$. (given $\pi^2=10$ )

Force between two point charges ${q}_{1}$ and ${q}_{2}$ placed in vacuum at $r$ $\mathrm{cm}$ apart is $F$. Force between them when placed in a medium having dielectric $K=5$ at $\frac{r}{5}$ $\mathrm{cm}$ apart will be:

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason(R) Assertion (A) : Work done by electric field on moving a positive charge on an equipotential surface is always zero. Reason (R) : Electric lines of forces are always perpendicular to equipotential surfaces. In the light of the above statements, choose the most appropriate answer from the options given below :

Given below are two statements: Statement I: Electromagnetic waves carry energy as they travel through space and this energy is equally shared by the electric and magnetic fields. Statement II: When electromagnetic waves strike a surface, a pressure is exerted on the surface. In the light of the above statements, choose the most appropriate answer from the options given below:

Given below are two statements: Statement I: In an LCR series circuit, current is maximum at resonance. Statement II: Current in a purely resistive circuit can never be less than that in a series LCR circuit when connected to same voltage source. In the light of the above statements, choose the correct from the options given below:

Given below are two statements : Statement (I) : When currents vary with time, Newton's third law is valid only if momentum carried by the electromagnetic field is taken into account. Statement (II) : Ampere's circuital law does not depend on Biot-Savart's law. In the light of the above statements, choose the correct answer from the options given below :

If frequency of electromagnetic wave is $60\mathrm{MHz}$ and it travels in air along $z$ direction then the corresponding electric and magnetic field vectors will be mutually perpendicular to each other and the wavelength of the wave $(\mathrm{in}m)$ is :

If the net electric field at point $\mathrm{P}$ along $\mathrm{Y}$ axis is zero, then the ratio of $\left|\frac{q_2}{q_3}\right|$ is $\frac{8}{5 \sqrt{x}}$, where $x=$ _____. 

In a co-axial straight cable, the central conductor and the outer conductor carry equal currents in opposite directions. The magnetic field is zero :

In a coil, the current changes from $-2 \mathrm{~A}$ to $+2 \mathrm{~A}$ in $0.2 \mathrm{~s}$ and induces an emf of $0.1 \mathrm{~V}$. The self inductance of the coil is :

In a metre-bridge when a resistance in the left gap is $2\Omega$ and unknown resistance in the right gap, the balance length is found to be $40\mathrm{cm}.$ On shunting the unknown resistance with $2\Omega ,$ the balance length changes by:

In a plane EM wave, the electric field oscillates sinusoidally at a frequency of $5\times {10}^{10}\mathrm{Hz}$ and an amplitude of $50V{m}^{–1}$. The total average energy density of the electromagnetic field of the wave is : [Use ${\epsilon }_{0}=8.85\times {10}^{–12}{C}^{2}{N}^{-1}{m}^{-2}$]

In an ac circuit, the instantaneous current is zero, when the instantaneous voltage is maximum. In this case, the source may be connected to : A. pure inductor. B. pure capacitor. C. pure resistor. D. combination of an inductor and capacitor. Choose the correct answer from the options given below :

In an a.c. circuit, voltage and current are given by: $V=100\mathrm{sin}(100t)V$ and $I=100\mathrm{sin}(100t+\frac{\pi }{3})\mathrm{mA}$ respectively. The average power dissipated in one cycle is :

In an ammeter, $5%$ of the main current passes through the galvanometer. If resistance of the galvanometer is $G,$ the resistance of ammeter will be:

In an electrical circuit drawn below the amount of charge stored in the capacitor is _______ $\mu C.$ 

In series LCR circuit, the capacitance is changed from $C$ to $4C$. To keep the resonance frequency unchanged, the new inductance should be :

In the experiment to determine the galvanometer resistance by half-deflection method, the plot of $1 / \theta$ vs the resistance $(\mathrm{R})$ of the resistance box is shown in the figure. The figure of merit of the galvanometer is _____ $\times 10^{-1} \mathrm{~A} /$ division. [The source has emf 2V] 

In the following circuit, the battery has an emf of $2V$ and an internal resistance of $\frac{2}{3}\Omega$. The power consumption in the entire circuit is ______ $W$. 

In the given circuit, the current flowing through the resistance $20\Omega$ is $0.3A$, while the ammeter reads $0.9A$. The value of ${R}_{1}$ is _____$\Omega$. 

In the given circuit, the current in resistance ${R}_{3}$ is: 

In the given circuit, the terminal potential difference of the cell is : 

In the given electromagnetic wave $\mathrm{E}_{\mathrm{y}}=600 \sin (\omega \mathrm{t}-\mathrm{kx}) \mathrm{Vm}^{-1}$, intensity of the associated light beam is (in $\mathrm{W} / \mathrm{m}^2$ : (Given $\epsilon_0=9 \times 10^{-12} \mathrm{C}^2 \mathrm{~N}^{-1} \mathrm{~m}^{-2}$ )

In the given figure an ammeter A consists of a $240 \Omega$ coil connected in parallel to a $10 \Omega$ shunt. The reading of the ammeter is $\qquad$ $\mathrm{mA}$ 

In the given figure $\mathrm{R}_1=10 \Omega, \mathrm{R}_2=8 \Omega, \mathrm{R}_3=4 \Omega$ and $\mathrm{R}_4=8 \Omega$. Battery is ideal with emf $12 \mathrm{~V}$. Equivalent resistant of the circuit and current supplied by battery are respectively : 

In the given figure, the charge stored in $6\mu F$ capacitor, when points $A$ and $B$ are joined by a connecting wire is _______$\mu C$. 

The electrostatic force between two point charges q₁ and q₂ separated by distance r is given by Coulomb's law as:

Match List-I with List-II : $\begin{array}{|c|c|c|c|} \hline & \text { List-I } & & \text { List-II } \\ \hline & \text { EM-Wave } & & \text { Wavelength Range } \\ \hline \text { (A) } & \text { Infra-red } & \text { (I) } & < 10^{-3} \mathrm{~nm} \\ \hline \text { (B) } & \text { Ultraviolet } & \text { (II) } & 400 \mathrm{~nm} \text { to } 1 \mathrm{~nm} \\ \hline \text { (C) } & \text { X-rays } S & \text { (III) } & 1 \mathrm{~mm} \text { to } 700 \mathrm{~nm} \\ \hline \text { (D) } & \text { Gamma rays } & \text { (IV) } & 1 \mathrm{~nm} \text { to } 10^{-3} \mathrm{~nm} \\ \hline \end{array}$

Match List-I with List-II :   Choose the correct answer from the options given below :

Match List I with List II  $\text { Choose the correct answer from the options given below: }$

Match List I with List II  Chose the correct answer from the options given below

Match 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>Gauss’s law of magnetostatics</td><td>i.</td><td>$\oint \vec{E}\cdot d\vec{a}=\frac{1}{{\epsilon }_{0}}\int \rho dV$</td></tr><tr><td>B.</td><td>Faraday’s law of electro magnetic induction</td><td>ii.</td><td>$\oint \vec{B}\cdot d\vec{a}=0$</td></tr><tr><td>C.</td><td>Ampere’s law</td><td>iii.</td><td>$\oint \vec{E}\cdot d\vec{l}=\frac{-d}{dt}\int \vec{B}\cdot d\vec{a}$</td></tr><tr><td>D.</td><td>Gauss’s law of electrostatics</td><td>iv.</td><td>$\oint \vec{B}\cdot d\vec{l}={\mu }_{0}I$</td></tr></tbody></table>Choose the correct answer from the options given below:

Paramagnetic substances: A. align themselves along the directions of external magnetic field. B. attract strongly towards external magnetic field. C. has susceptibility little more than zero. D. move from a region of strong magnetic field to weak magnetic field. Choose the most appropriate answer from the options given below:

Primary coil of a transformer is connected to $220VAC$. Primary and secondary turns of the transforms are $100$ and $10$ respectively. Secondary coil of transformer is connected to two series resistances as shown in figure. The output voltage $({V}_{0})$ is : 

Ques: $\sigma$ is the uniform surface charge density of a thin spherical shell of radius $R$. The electric field at any point on the surface of the spherical shell is :

Resistance of a wire at $0^{\circ} \mathrm{C}, 100^{\circ} \mathrm{C}$ and $t^{\circ} \mathrm{C}$ is found to be $10 \Omega, 10.2 \Omega$ and $10.95 \Omega$ respectively. The temperature $t$ in Kelvin scale is _________

Suppose a uniformly charged wall provides a uniform electric field of $2\times {10}^{4}N{C}^{-1}$ normally. A charged particle of mass $2g$ being suspended through a silk thread of length $20\mathrm{cm}$ and remain stayed at a distance of $10\mathrm{cm}$ from the wall. Then the charge on the particle will be $\frac{1}{\sqrt{x}}\mu C$ where $x=$ ________ [use $g=10m{s}^{-2}$]

The charge accumulated on the capacitor connected in the following circuit is ______\mu C. (Given $C=150\mu F)$ 

The coercivity of a magnet is $5 \times 10^3 \mathrm{~A} / \mathrm{m}$. The amount of current required to be passed in a solenoid of length $30 \mathrm{~cm}$ and the number of turns 150 , so that the magnet gets demagnetised when inside the solenoid is _____A.

The current flowing through the $1 \Omega$ resistor is $\frac{n}{10}$ A. The value of $n$ is _________ 

The current in a conductor is expressed as $I=3{t}^{2}+4{t}^{3}$, where $I$ is in Ampere and $t$ is in second. The amount of electric charge that flows through a section of the conductor during $t=1s$ to $t=2s$ is ____________ $C.$

The current in an inductor is given by $\mathrm{I}=(3 \mathrm{t}+8)$ where $\mathrm{t}$ is in second. The magnitude of induced emf produced in the inductor is $12 \mathrm{mV}$. The self-inductance of the inductor _____ $\mathrm{mH}$.

The current of $5A$ flows in a square loop of sides $1m$ is placed in air. The magnetic field at the centre of the loop is $X\sqrt{2}\times {10}^{-7}T$. The value of $X$ is _________.

The deflection in moving coil galvanometer falls from $25$ divisions to $5$ division when a shunt of $24\Omega$ is applied. The resistance of galvanometer coil will be:

The distance between charges $+q$ and $-q$ is $2l$ and between $+2q$ and $-2q$ is $4l$. The electrostatic potential at point $P$ at a distance $r$ from centre $O$ is $-\alpha [\frac{ql}{{r}^{2}}]\times {10}^{9}V$, where the value of $\alpha$ is ______. (Use $\frac{1}{4\pi {\epsilon }_{0}}=9\times {10}^{9}N{m}^{2}{C}^{-2}$) 

The effective resistance between $A$ and $B$, if resistance of each resistor is $R$, will be 

The electric current through a wire varies with time as $I={I}_{0}+\beta t$, where ${I}_{0}=20A$ and $\beta =3A{s}^{-1}$. The amount of electric charge crossed through a section of the wire in $20s$ is:

The electric field at point $\mathrm{p}$ due to an electric dipole is $\mathrm{E}$. The electric field at point $\mathrm{R}$ on equitorial line will be $\frac{\mathrm{E}}{x}$. The value of $x$ : 

The electric field between the two parallel plates of a capacitor of $1.5 \mu \mathrm{F}$ capacitance drops to one third of its initial value in $6.6 \mu \mathrm{s}$ when the plates are connected by a thin wire. The resistance of this wire is _____$\Omega$. (Given, $\log 3=1.1$ )

The electric field in an electromagnetic wave is given by $\overrightarrow{\mathrm{E}}=\hat{i} 40 \cos \omega(\mathrm{t}-z / \mathrm{c}) \mathrm{NC}^{-1}$. The magnetic field induction of this wave is (in SI unit) :

The electric field of an electromagnetic wave in free space is represented as $\vec{E}={E}_{0}\mathrm{cos}(\omega t-kz)\hat{i}$. The corresponding magnetic induction vector will be :

The electric potential at the surface of an atomic nucleus $(Z=50)$ of radius $9\times {10}^{-13}\mathrm{cm}$ is $\alpha \times {10}^{6}V$. What is the value of $\alpha$? (Charge of proton $1.6\times {10}^{-19}C$)

The electrostatic force $\left(\overrightarrow{F_1}\right)$ and magnetic force $\left(\vec{F}_2\right)$ acting on a charge $q$ moving with velocity $v$ can be written :

The electrostatic potential due to an electric dipole at a distance $r$ varies as :

The equivalent resistance between $\mathrm{A}$ and $\mathrm{B}$ is : 

The horizontal component of earth's magnetic field at a place is $3.5\times {10}^{-5}T$. A very long straight conductor carrying current of $\sqrt{2}A$ in the direction from South east to North West is placed. The force per unit length experienced by the conductor is ________$\times {10}^{-6}N{m}^{-1}$.

The magnetic field at the centre of a wire loop formed by two semicircular wires of radii ${R}_{1}=2\pi m$ and ${R}_{2}=4\pi m$ carrying current $I=4A$ as per figure given below is $\alpha \times {10}^{-7}T$. The value of $\alpha$ is _____. (Centre $O$ is common for all segments) 

The magnetic field existing in a region is given by $\vec{B}=0.2(1+2 x) \hat{k} \mathrm{~T}$. A square loop of edge $50 \mathrm{~cm}$ carrying 0.5 A current is placed in $x-y$ plane with its edges parallel to the $x-y$ axes, as shown in figure. The magnitude of the net magnetic force experienced by the loop is_____ $\mathrm{mN}$. 

The magnetic field in a plane electromagnetic wave is $\mathrm{B}_{\mathrm{y}}=\left(3.5 \times 10^{-7}\right) \sin \left(1.5 \times 10^3 x+0.5 \times 10^{11} t\right) \mathrm{T}$. The corresponding electric field will be :

The magnetic flux $\phi$ (in weber) linked with a closed circuit of resistance $8\Omega$ varies with time (in seconds) as $\phi =5{t}^{2}-36t+1$. The induced current in the circuit at $t=2s$ is _______ $A$.

The magnetic moment of a bar magnet is $0.5 \mathrm{Am}^2$. It is suspended in a uniform magnetic field of $8 \times 10^{-2} \mathrm{~T}$. The work done in rotating it from its most stable to most unstable position is:

The magnetic potential due to a magnetic dipole at a point on its axis situated at a distance of $20\mathrm{cm}$ from its center is $1.5\times {10}^{-5}Tm$. The magnetic moment of the dipole is _______ $A{m}^{2}$. (Given : $\frac{{\mu }_{0}}{4\pi }={10}^{-7}Tm{A}^{-1}$)

The number of electrons flowing per second in the filament of a $110 \mathrm{~W}$ bulb operating at $220 \mathrm{~V}$ is : $\left(\right.$ Given $\left.\mathrm{e}=1.6 \times 10^{-19} \mathrm{C}\right)$

The primary side of a transformer is connected to $230V,50\mathrm{Hz}$ supply. The turn ratio of primary to secondary winding is $10:1$. Load resistance connected to the secondary side is $46\Omega$. The power consumed in it is:

The ratio of heat dissipated per second through the resistance $5 \Omega$ and $10 \Omega$ in the circuit given below is : 

The reading in the ideal voltmeter $(V)$ shown in the given circuit diagram is: 

The resistance per centimeter of a meter bridge wire is $r$, with $X\Omega$ resistance in left gap. Balancing length from left end is at $40\mathrm{cm}$ with $25\Omega$ resistance in right gap. Now the wire is replaced by another wire of $2r$ resistance per centimeter. The new balancing length for same settings will be at

The value of unknown resistance $(x)$ for which the potential difference between $B$ and $D$ will be zero in the arrangement shown, is : 

The vehicles carrying inflammable fluids usually have metallic chains touching the ground :

Three capacitors of capacitances $25 \mu \mathrm{F}, 30 \mu \mathrm{F}$ and $45 \mu \mathrm{F}$ are connected in parallel to a supply of $100 \mathrm{~V}$. Energy stored in the above combination is E. When these capacitors are connected in series to the same supply, the stored energy is $\frac{9}{x} \mathrm{E}$. The value of $x$ is _____.

Three infinitely long charged thin sheets are placed as shown in figure. The magnitude of electric field at the point $P$ is $\frac{x \sigma}{\epsilon_o}$. The value of $x$ is _______ (all quantities are measured in SI units). 

Three voltmeters, all having different internal resistances are joined as shown in figure. When some potential difference is applied across $A$ and $B$, their readings are ${V}_{1},{V}_{2}$ and ${V}_{3}$. Choose the correct option. 

To determine the resistance $(R)$ of a wire, a circuit is designed below. The $V-I$ characteristic curve for this circuit is plotted for the voltmeter and the ammeter readings as shown in figure. The value of $R$ is ______ $\Omega$. 

To measure the internal resistance of a battery, potentiometer is used. For $\mathrm{R}=10 \Omega$, the balance point is observed at $l=500 \mathrm{~cm}$ and for $\mathrm{R}=1 \Omega$ the balance point is observed at $l=400 \mathrm{~cm}$. The internal resistance of the battery is approximately :

To measure the temperature coefficient of resistivity $\alpha$ of a semiconductor, an electrical arrangement shown in the figure is prepared. The arm $\mathrm{BC}$ is made up of the semiconductor. The experiment is being conducted at $25^{\circ}C$ and resistance of the semiconductor arm is $3m\Omega$. Arm $\mathrm{BC}$ is cooled at a constant rate of $2^{\circ}C{s}^{-1}$. If the galvanometer $G$ shows no deflection after $10s,$ then $\alpha$ is: 

Twelve wires each having resistance $2 \Omega$ are joined to form a cube. A battery of $6 \mathrm{~V}$ emf is joined across point $a$ and $c$. The voltage difference between $e$ and $f$ is ______V. 

Two cells are connected in opposition as shown. Cell ${E}_{1}$ is of $8V$ emf and $2\Omega$ internal resistance; the cell ${E}_{2}$ is of $2V$ emf and $4\Omega$ internal resistance. The terminal potential difference of cell ${E}_{2}$ is ______ $V$. 

Two charged conducting spheres of radii $a$ and $b$ are connected to each other by a conducting wire. The ratio of charges of the two spheres respectively is:

Two charges $q$ and $3q$ are separated by a distance ‘$r$’ in air. At a distance $x$ from charge $q$, the resultant electric field is zero. The value of $x$ is :

Two charges of $-4\mu C$ and $+4\mu C$ are placed at the points $A(1,0,4)m$ and $B(2,-1,5)m$ located in an electric field $\vec{E}=0.20\hat{i}V{\mathrm{cm}}^{-1}$. The magnitude of the torque acting on the dipole is $8\sqrt{\alpha }\times {10}^{-5}Nm$, where $\alpha =$_________.

Two charges of $5Q$ and $-2Q$ are situated at the points $(3a,0)$ and $(-5a,0)$ respectively. The electric flux through a sphere of radius $4a$ having centre at origin is:

Two circular coils $P$ and $Q$ of $100$ turns each have same radius of $\pi \mathrm{cm}$. The currents in $P$ and $R$ are $1A$ and $2A$ respectively. $P$ and $Q$ are placed with their planes mutually perpendicular with their centers coincide. The resultant magnetic field induction at the center of the coils is $\sqrt{x}\mathrm{mT}$, where $x=$ ______. [Use ${\mu }_{0}=4\pi \times {10}^{-7}Tm{A}^{-1}$]

Two coils have mutual inductance $0.002H$. The current changes in the first coil according to the relation $i={i}_{0}sin\omega t$, where ${i}_{0}=5A$ and $\omega =50\pi$ $\mathrm{rad}{s}^{-1}$. The maximum value of $\mathrm{emf}$ in the second coil is $\frac{\pi }{\alpha }V$. The value of $\alpha$ is

Two conducting circular loops A and B are placed in the same plane with their centers coinciding as shown in figure. The mutual inductance between them is : 

Two identical capacitors have same capacitance $C$. One of them is charged to the potential $V$ and other to the potential $2V$. The negative ends of both are connected together. When the positive ends are also joined together, the decrease in energy of the combined system is :

Two identical charged spheres are suspended by strings of equal lengths. The string make an angle of $37^{\circ}$ with each other. When suspended in a liquid of density $0.7g{\mathrm{cm}}^{-3}$, the angle remains same. If density of material of the sphere is $1.4g{\mathrm{cm}}^{-3}$, the dielectric constant of the liquid is _____ $(\mathrm{tan}37^{\circ}=\frac{3}{4})$

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle $\theta$ with each other. When suspended in water the angle remains the same. If density of the material of the sphere is $1.5g/\mathrm{cc},$ the dielectric constant of water will be ______. (Take density of water $=1g/\mathrm{cc}$)

Two identical conducting spheres $P$ and $S$ with charge $Q$ on each, repel each other with a force $16 \mathrm{~N}$. A third identical uncharged conducting sphere $R$ is successively brought in contact with the two spheres. The new force of repulsion between $\mathrm{P}$ and $\mathrm{S}$ is :

Two insulated circular loop $A$ and $B$ radius $a$ carrying a current of $I$ in the anti clockwise direction as shown in figure. The magnitude of the magnetic induction at the centre will be: 

Two long, straight wires carry equal currents in opposite directions as shown in figure. The separation between the wires is $5.0\mathrm{cm}$. The magnitude of the magnetic field at a point $P$ midway between the wires is $_____\mu T$. (Given: ${\mu }_{0}=4\pi \times {10}^{-7}Tm{A}^{-1}$) 

Two parallel long current carrying wire separated by a distance $2 r$ are shown in the figure. The ratio of magnetic field at $A$ to the magnetic field produced at $C$ is $\frac{x}{7}$. The value of $x$ is _____ 

Two particles $X$ and $Y$ having equal charges are being accelerated through the same potential difference. Thereafter, they enter normally in a region of uniform magnetic field and describes circular paths of radii ${R}_{1}$ and ${R}_{2}$ respectively. The mass ratio of $X$ and $Y$ is :

Two resistance of $100\Omega$ and $200\Omega$ are connected in series with a battery of $4V$ and negligible internal resistance. A voltmeter is used to measure voltage across $100\Omega$ resistance, which gives reading as $1V$. The resistance of voltmeter must be _______ $\Omega$.

Two wires $A$ and $B$ are made up of the same material and have the same mass. Wire $A$ has radius of $2.0 \mathrm{~mm}$ and wire $B$ has radius of $4.0 \mathrm{~mm}$. The resistance of wire $B$ is $2 \Omega$. The resistance of wire $A$ is _____$\Omega$.

Water boils in an electric kettle in 20 minutes after being switched on. Using the same main supply, the length of the heating element should be _____ to _____ times of its initial length if the water is to be boiled in 15 minutes.

Wheatstone bridge principle is used to measure the specific resistance $({S}_{1})$ of given wire, having length $L$, radius $r$. If $X$ is the resistance of wire, then specific resistance is : ${S}_{1}=X(\frac{\pi {r}^{2}}{L})$. If the length of the wire gets doubled then the value of specific resistance will be :

When a coil is connected across a $20 \mathrm{~V}$ dc supply, it draws a current of $5 \mathrm{~A}$. When it is connected across $20 \mathrm{~V}, 50 \mathrm{~Hz}$ ac supply, it draws a current of $4 \mathrm{~A}$. The self inductance of the coil is ______ $\mathrm{mH}$. $($ Take $\pi=3$ )

When a potential difference $V$ is applied across a wire of resistance $R$, it dissipates energy at a rate $W.$ If the wire is cut into two halves and these halves are connected mutually parallel across the same supply, the energy dissipation rate will become:

When a $d c$ voltage of $100 \mathrm{~V}$ is applied to an inductor, a $d c$ current of $5 \mathrm{~A}$ flows through it. When an ac voltage of $200 \mathrm{~V}$ peak value is connected to inductor, its inductive reactance is found to be $20 \sqrt{3} \Omega$. The power dissipated in the circuit is _______ W.