JEE Main 2022 — Electromagnetism

A $220V,50\mathrm{Hz}$ AC source is connected to a $25V,5W$ lamp and an additional resistance $R$ in series (as shown in figure) to run the lamp at its peak brightness, then the value of $R$ (in ohm) will be 

A bar magnet having a magnetic moment of $2.0\times {10}^{5}J{T}^{-1}$, is placed along the direction of uniform magnetic field of magnitude $B=14\times {10}^{-5}T$. The work done in rotating the magnet slowly through $60^{\circ}$ from the direction of field is

A battery of $6V$ is connected to the circuit as shown below. The current $I$ drawn from the battery is 

A beam of light travelling along $X$-axis is described by the electric field ${E}_{y}=900\mathrm{sin}\omega (t-\frac{x}{c})$. The ratio of electric force to magnetic force on a charge $q$ moving along $Y$-axis with a speed of $3\times {10}^{7}m{s}^{-1}$ will be : [Given speed of light $=3\times {10}^{8}m{s}^{-1}$ ]

A capacitor is discharging through a resistor $R$. Consider in time ${t}_{1}$, the energy stored in the capacitor reduces to half of its initial value and in time ${t}_{2}$, the charge stored reduces to one eighth of its initial value. The ratio $\frac{{t}_{1}}{{t}_{2}}$ will be

A capacitor of capacitance $50\mathrm{pF}$ is charged by $100V$ source. It is then connected to another uncharged identical capacitor. Electrostatic energy loss in the process is____ $\mathrm{nJ}$.

A capacitor of capacitance $500\mu F$ is charged completely using a de supply of $100V$. It is now connected to an inductor of inductance $50\mathrm{mH}$ to form an LC circuit. The maximum current in LC circuit will be _____ $A$.

A capacitor ${C}_{1}$ of capacitance $5\mu F$ is charged to a potential of $30V$ using a battery. The battery is then removed and the charged capacitor is connected to an uncharged capacitor ${C}_{2}$ of capacitance $10\mu F$ as shown in figure. When the switch is closed charge flows between the capacitors. At equilibrium, the charge on the capacitor ${C}_{2}$ is _____ $\mu C$. 

A charge of $4\mu C$ is to be divided into two. The distance between the two divided charges is constant. The magnitude of the divided charges so that the force between them is maximum, will be:

A charge particle is moving in a uniform magnetic field $(2\hat{i}+3\hat{j})T$. If it has an acceleration of $(\alpha \hat{i}-4\hat{j})m{s}^{-2}$, then the value of $\alpha$ will be

A circuit element $X$ when connected to an AC supply of peak voltage $100V$ gives a peak current of $5A$ which is in phase with the voltage. A second element $Y$ when connected to the same AC supply also gives the same value of peak current which lags behind the voltage by $\frac{\pi }{2}$. If $X$ and $Y$ are connected in series to the same supply, what will be the rms value of the current in ampere?

A circular coil of 1000 turns each with area $1{m}^{2}$ is rotated about its vertical diameter at the rate of one revolution per second in a uniform horizontal magnetic field of $0.07T$. The maximum voltage generation will be _____ $V$.

A closely wounded circular coil of radius $5\mathrm{cm}$ produces a magnetic field of $37.68\times {10}^{-4}T$ at its center. The current through the coil is _____ $A$. [Given, number of turns in the coil is $100$ and $\pi =3.14$]

A $10\Omega ,20\mathrm{mH}$ coil carrying constant current is connected to a battery of $20V$ through a switch. Now after switch is opened current becomes zero in $100\mu s$. The average e.m.f. induced in the coil is _____ $V$.

A coil is placed in a time varying magnetic field. If the number of turns in the coil were to be halved and the radius of wire doubled, the electrical power dissipated due to the current induced in the coil would be (Assume the coil to be short circuited.)

A coil of inductance $1H$ and resistance $100\Omega$ is connected to a battery of $6V$. Determine approximately : (a) The time elapsed before the current acquires half of its steady-state value (b) The energy stored in the magnetic field associated with the coil at an instant $15\mathrm{ms}$ after the circuit is switched on. (Given $\mathrm{ln}2=0.693$, ${e}^{\frac{-3}{2}}=0.25$)

A composite parallel plate capacitor is made up of two different dielectric materials with different thickness (${t}_{1}$ and ${t}_{2}$) as shown in figure. The two different dielectric material are separated by a conducting foil $F$. The voltage of the conducting foil is _____ $V$. 

A condenser of $2\mu F$ capacitance is charged steadily from $0$ to $5C$. Which of the following graph represents correctly the variation of potential difference$(V)$ across its plates with respect to the charge $(Q)$ on the condenser?

A conducting circular loop is placed in $X-Y$ plane in presence of magnetic field $\vec{B}=(3{t}^{3}\hat{j}+3{t}^{2}\hat{k})$ in SI unit. If the radius of the loop is $1m$, the induced emf in the loop, at time, $t=2s$ is $n\pi V$. The value of $n$ is _____ .

A current of $15\mathrm{mA}$ flows in the circuit as shown in figure. The value of potential difference between the points $A$ and $B$ will be 

A deuteron and a proton moving with equal kinetic energy enter into to a uniform magnetic field at right angle to the field. If ${r}_{d}$ and ${r}_{p}$ are the radii of their circular paths respectively, then the ratio $\frac{{r}_{d}}{{r}_{p}}$ will be $\sqrt{x}:1$ where $x$ is _____ .

A direct current of $4A$ and an alternating current of peak value $4A$ flow through resistance of $3\Omega$ and $2\Omega$ respectively. The ratio of heat produced in the two resistances in same interval of time will be :

A force of $10N$ acts on a charged particle placed between two plates of a charged capacitor. If one plate of capacitor is removed, then the force acting on that particle will be.

A $72\Omega$ galvanometer is shunted by a resistance of $8\Omega$. The percentage of the total current which passes through the galvanometer is

A $1m$ long copper wire carries a current of $1A$. If the cross section of the wire is $2.0{\mathrm{mm}}^{2}$ and the resistivity of copper is $1.7\times {10}^{-8}\Omega m$. The force experienced by moving electron in the wire is _____$\times {10}^{-23}N$ (Charge of electron$=1.6\times {10}^{-19}C$ )

A long cylindrical volume contains a uniformly distributed charge of density $\rho C{m}^{-3}$. The electric field inside the cylindrical volume at a distance $x=\frac{2{\epsilon }_{0}}{\rho }m$ from its axis is _____ $V{m}^{-1}$. 

A long cylindrical volume contains a uniformly distributed charge of density $\rho$. The radius of cylindrical volume is $R$. A charge particle $(q)$ revolves around the cylinder in a circular path. The kinetic energy of the particle is :

A long solenoid carrying a current produces a magnetic field $B$ along its axis. If the current is doubled and the number of turns per $\mathrm{cm}$ is halved, the new value of magnetic field will be equal to

A long straight wire with a circular cross-section having radius $R$, is carrying a steady current $I$. The current $I$ is uniformly distributed across this cross-section. Then the variation of magnetic field due to current $I$ with distance $r(r<R)$ from its centre will be

A $1m$ long wire is broken into two unequal parts $X$ and $Y$. The $X$ part of the wire is stretched into another wire $W$. Length of $W$ is twice the length of $X$ and the resistance of $W$ is twice that of $Y$. Find the ratio of length of $X$ and$Y$.

A metal surface is illuminated by a radiation of wavelength $4500\overset{\circ }{A}$. The ejected photo-electron enters a constant magnetic field of $2\mathrm{mT}$ making an angle of $90^{\circ}$ with the magnetic field. If it starts revolving in a circular path of radius $2\mathrm{mm}$, the work function of the metal is approximately

A metallic conductor of length $1m$ rotates in a vertical plane parallel to east-west direction about one of its end with angular velocity $5\mathrm{rad}{s}^{-1}$. If the horizontal component of earth's magnetic field is $0.2\times {10}^{-4}T$, then emf induced between the two ends of the conductor is

A meter bridge setup is shown in the figure. It is used to determine an unknown resistance $R$ using a given resistor of $15\Omega$. The galvanometer $(G)$ shows null defection when tapping key is at $43\mathrm{cm}$ mark from end $A$. If the end correction for end $A$ is $2\mathrm{cm}$, then the determined value of $R$ will be $\Omega$. 

A parallel plate capacitor filled with a medium of dielectric constant $10$, is connected across a battery and is charged. The dielectric slab is replaced by another slab of dielectric constant $15$. Then the energy of capacitor will

A parallel plate capacitor is formed by two plates each of area $30\pi {\mathrm{cm}}^{2}$ separated by $1\mathrm{mm}$. A material of dielectric strength $3.6\times {10}^{7}V{m}^{-1}$ is filled between the plates. If the maximum charge that can be stored on the capacitor without causing any dielectric breakdown is $7\times {10}^{-6}C$, the value of dielectric constant of the material is : [Use $\frac{1}{4\pi {\epsilon }_{o}}=9\times {10}^{9}N{m}^{2}{C}^{-2}$]

A parallel plate capacitor is made up of stair like structure with a plate area A of each stair and that is connected with a wire of length $b$, as shown in the figure. The capacitance of the arrangement is $\frac{x}{15}\frac{{\epsilon }_{0}A}{b}$, The value of $x$ is _____ . 

A parallel plate capacitor with plate area $A$ and plate separation $d=2m$ has a capacitance of $4\mu F$. The new capacitance of the system if half of the space between them is filled with a dielectric material of dielectric constant $K=3$ (as shown in figure) will be 

A parallel plate capacitor with width $4\mathrm{cm}$, length $8\mathrm{cm}$ and separation between the plates of $4\mathrm{mm}$ is connected to a battery of $20V$. A dielectric slab of dielectric constant $5$ having length $1\mathrm{cm}$, width $4\mathrm{cm}$ and thickness $4\mathrm{mm}$ is inserted between the plates of parallel plate capacitor. The electrostatic energy of this system will be _____ ${\epsilon }_{0}J$. (Where ${\epsilon }_{0}$ is the permittivity of free space)

A plane electromagnetic wave travels in a medium of relative permeability $1.61$ and relative permittivity $6.44$. If magnitude of magnetic intensity is $4.5\times {10}^{-2}A{m}^{-1}$ at a point, what will be the approximate magnitude of electric field intensity at that point ? (Given : Permeability of free space ${\mu }_{0}=4\pi \times {10}^{-7}N{A}^{-2}$, speed of light in vacuum $c=3\times {10}^{8}{ms}^{-1}$)

A positive charge particle of $100\mathrm{mg}$ is thrown in opposite direction to a uniform electric field of strength $1\times {10}^{5}N{C}^{-1}$. If the charge on the particle is $40\mu C$ and the initial velocity is $200{ms}^{-1}$, how much distance it will travel before coming to the rest momentarily

A proton, a deuteron and an $\alpha$-particle with same kinetic energy enter into a uniform magnetic field at right angle to magnetic field. The ratio of the radii of their respective circular paths is :

A proton and an alpha particle of the same velocity enter in a uniform magnetic field which is acting perpendicular to their direction of motion. The ratio of the radii of the circular paths described by the alpha particle and proton is

A resistance of $40\Omega$ is connected to a source of alternating current rated $220V,50\mathrm{Hz}$. Find the time taken by the current to change from its maximum value to the rms value :

A resistor develops $300J$ of thermal energy in $15s$, when a current of $2A$ is passed through it. If the current increases to $3A$, the energy developed in $10s$ is _____ $J$.

A series LCR circuit has $L=0.01H,R=10\Omega$ and $C=1\mu F$ and it is connected to ac voltage of amplitude $({V}_{m})50V$. At frequency $60%$ lower than resonant frequency, the amplitude of current will be approximately

A singly ionized magnesium atom $(A=24)$ ion is accelerated to kinetic energy $5\mathrm{keV}$, and is projected perpendicularly into a magnetic field $B$ of the magnitude $0.5T$. The radius of path formed will be _____ $\mathrm{cm}.$

A sinusoidal voltage $V(t)=210\mathrm{sin}3000t$ volt is applied to a series LCR circuit in which $L=10\mathrm{mH},C=25\mu F$ and $R=100\Omega$. The phase difference $(\Phi )$ between the applied voltage and resultant current will be

A slab of dielectric constant $K$ has the same crosssectional area as the plates of a parallel plate capacitor and thickness $\frac{3}{4}d$, where $d$ is the separation of the plates. The capacitance of the capacitor when the slab is inserted between the plates will be : (Given ${C}_{0}=$ capacitance of capacitor with air as medium between plates.)

A small square loop of wire of side $l$ is placed inside a large square loop of wire $L(L\gg l)$. Both loops are coplanar and their centres coincide at point $O$ as shown in figure. The mutual inductance of the system is 

A $110V,50\mathrm{Hz},\mathrm{AC}$ source is connected in the circuit (as shown in figure). The current through the resistance $55\Omega$, at resonance in the circuit, will be _____$A$. 

A source of potential difference $V$ is connected to the combination of two identical capacitors as shown in the figure. When key $K$ is closed, the total energy stored across the combination is ${E}_{1}$. Now key $K$ is opened and dielectric of dielectric constant $5$ is introduced between the plates of the capacitors. The total energy stored across the combination is now ${E}_{2}$. The ratio $\frac{{E}_{1}}{{E}_{2}}$ will be 

A spherically symmetric charge distribution is considered with charge density varying as $\rho (r)={\begin{matrix}{\rho }_{0}(\frac{3}{4}-\frac{r}{R}) & \text{ for }r\leq R \\ \mathrm{Zero} & & & \mathrm{for}r>R\end{matrix}$ Where, $r(r<R)$ is the distance from the centre $O$ (as shown in figure). The electric field at point $P$ will be : 

A teacher in his physics laboratory allotted an experiment to determine the resistance $(G)$ a galvanometer. Students took the observations for $\frac{1}{3}$ deflection in the galvanometer. Which of the below is true for measuring value of $G$?

A telegraph line of length $100\mathrm{km}$ has a capacity of $0.01\mu F{\mathrm{km}}^{-1}$ and it carries an alternating current at $0.5$ kilo cycle per second. If minimum impedance is required, then the value of the inductance that needs to be introduced in series is _____ $\mathrm{mH}$. (If $\pi =\sqrt{10}$)

A. The drift velocity of electrons decreases with the increase in the temperature of conductor. B. The drift velocity is inversely proportional to the area of cross-section of given conductor. C. The drift velocity does not depend on the applied potential difference to the conductor. D. The drift velocity of electron is inversely proportional to the length of the conductor. E. The drift velocity increases with the increase in the temperature of conductor. Choose the correct answer from the options given below:

A transformer operating at primary voltage $8\mathrm{kV}$ and secondary voltage $160V$ serves a load of $80\mathrm{kW}$. Assuming the transformer to be ideal with purely resistive load and working on unity power factor, the loads in the primary and secondary circuit would be

A triangular shaped wire carrying $10A$ current is placed in a uniform magnetic field of $0.5T$, as shown in figure. The magnetic force on segment $CD$ is (Given $BC=CD=BD=5\mathrm{cm}$). 

A uniform electric field $E=(\frac{8m}{e})V{m}^{-1}$ is created between two parallel plates of length $1m$ as shown in figure, (where $m=$ mass of electron and $e=$ charge of electron). An electron enters the field symmetrically between the plates with a speed of $2m{s}^{-1}$. The angle of the deviation $(\theta )$ of the path of the electron as it comes out of the field will be _____ . 

A velocity selector consists of electric field $\vec{E}=E\hat{k}$ and magnetic field $\vec{B}=B\hat{j}$ with $B=12\mathrm{mT}$. The value $E$ required for an electron of energy $728\mathrm{eV}$ moving along the positive $x$-axis to pass undeflected is (Given, mass of electron $=9.1\times {10}^{-31}\mathrm{kg}$)

A vertical electric field of magnitude $4.9\times {10}^{5}N{C}^{-1}$ just prevents a water droplet of a mass $0.1g$ from falling. The value of charge on the droplet will be : (Given $g=9.8m{s}^{-2}$)

A wire $X$ of length $50\mathrm{cm}$ carrying a current of $2A$ is placed parallel to a long wire $Y$ of length $5m$. The wire $Y$ carries a current of $3A$. The distance between two wires is $5\mathrm{cm}$ and currents flow in the same direction. The force acting on the wire $Y$ is : 

A wire of length $314\mathrm{cm}$ carrying current of $14A$ is bent to form a circle. The magnetic moment of the coil is $A-{m}^{2}$. [Given $\pi =3.14$]

A wire of resistance ${R}_{1}$$R_{1}$ is drawn out so that its length is increased by twice of its original length. The ratio of new resistance to original resistance is:

All resistances in figure are $1\Omega$ each. The value of current '$I$' is $\frac{a}{5}A$. The value of $a$ is _____ . 

An AC source is connected to an inductance of $100\mathrm{mH}$, a capacitance of $100\mu F$ and a resistance of $120\Omega$ as shown in figure. The time in which the resistance having a thermal capacity $2JC-1\circ$ will get heated by $16^{\circ}C$ is _____ $s$. 

An alternating emf $E=440\mathrm{sin}100\pi t$ is applied to a circuit containing an inductance of $\frac{\sqrt{2}}{\pi }H$. If an a.c. ammeter is connected in the circuit, its reading will be :

An aluminium wire is stretched to make its length, $0.4%$ larger. The percentage change in resistance is

An electric bulb is rated as $200W$. What will be the peak magnetic field at $4m$ distance produced by the radiations coming from this bulb? Consider this bulb as a point source with $3.5%$ efficiency.

An electrical bulb rated $220V,100W$, is connected in series with another bulb rated $220V$, $60W$. If the voltage across combination is $220V$, the power consumed by the $100W$ bulb will be about _____ $W$.

An EM wave propagating in $x$-direction has a wavelength of $8\mathrm{mm}$. The electric field vibrating $y$-direction has maximum magnitude of $60{\mathrm{Vm}}^{-1}$. Choose the correct equations for electric and magnetic fields if the EM wave is propagating in vacuum :

An inductor of $0.5\mathrm{mH}$, a capacitor of $200\mu F$ and a resistor of $2\Omega$ are connected in series with a $220V$ ac source. If the current is in phase with the emf, the frequency of ac source will be ______$\times {10}^{2}\mathrm{Hz}$.

An infinitely long hollow conducting cylinder with radius $R$ carries a uniform current along its surface. Choose the correct representation of magnetic field $(B)$as a function of radial distance $(r)$ from the axis of cylinder.

${B}_{X}$ and ${B}_{Y}$ are the magnetic field at the centre of two coils of two coils $X$ and $Y$ respectively, each carrying equal current. If coil $X$ has $200$ turns and $20\mathrm{cm}$ radius and coil $Y$ has $400$ turns and $20\mathrm{cm}$ radius, the ratio of ${B}_{X}$ and ${B}_{Y}$ is

As show in the figure, in steady state, the charge stored in the capacitor is _____$\times {10}^{-6}C$. 

As shown in the figure, a metallic rod of linear density $0.45\mathrm{kg}{m}^{-1}$ is lying horizontally on a smooth incline plane which makes an angle of $45^{\circ}$ with the horizontal. The minimum current flowing in the rod required to keep it stationary, when $0.15T$ magnetic field is acting on it in the vertical upward direction, will be (Use $g=10m{s}^{-2}$) 

As shown in the figure an inductor of inductance $200\mathrm{mH}$ is connected to an $\mathrm{AC}$ source of emf $220V$and frequency $50\mathrm{Hz}$. The instantaneous voltage of the source is $0V$ when the peak value of current is $\frac{\sqrt{a}}{\pi }A$. The value of $a$ is _____ . 

Capacitance of an isolated conducting sphere of radius ${R}_{1}$ becomes $n$ times when it is enclosed by a concentric conducting sphere of radius ${R}_{2}$ connected to earth. The ratio of their radii $(\frac{{R}_{2}}{{R}_{1}})$ is:

Current measured by the ammeter $(A)$ in the reported circuit when no current flows through $10\Omega$ resistance, will be _____ $A$. 

Eight copper wire of length $l$ and diameter d are joined in parallel to form a single composite conductor of resistance $R$. If a single copper wire of length $2l$ have the same resistance $(R)$ then its diameter will be _____ $d$.

Two point charges +q and -q are placed at distance d apart. The electric field at the midpoint of the line joining them is:

Find the equivalent resistance between point $A$ and $B$ 

For a series $LCR$ circuit, $I$ vs $\omega$ curve is shown  (a) To the left of ${\omega }_{r}$, the circuit is mainly capacitive. (b) To the left of ${\omega }_{r}$, the circuit is mainly inductive. (c) At ${\omega }_{r}$, impedance of the circuit is equal to the resistance of the circuit. (d) At ${\omega }_{r}$, impedance of the circuit is $0$. Choose the most appropriate answer from the options given below.

For the given circuit the current through battery of $6V$ just after closing the switch '$S$' will be _____ $A$. 

For the network shown below, the value of ${V}_{B}-{V}_{A}$ is _____ $V$. 

Given below are two statements : One is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : In an uniform magnetic field, speed and energy remains the same for a moving charged particle. Reason (R): Moving charged particle experiences magnetic force perpendicular to its direction of motion.

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: Alloys such as constantan and manganin are used in making standard resistance coils. Reason R: Constantan and manganin have very small value of temperature coefficient of resistance. In the light of the above statements, choose the correct answer from the options given below.

Given below are two statements : Statement - I : Susceptibilities of paramagnetic and ferromagnetic substances increase with decrease in temperature. Statement - II : Diamagnetism is a result of orbital motions of electrons developing magnetic moments opposite to the applied magnetic field. Choose the correct answer from the options given below

Given below are two statements : Statement I : A uniform wire of resistance $80\Omega$ is cut into four equal parts. These parts are now connected in parallel. The equivalent resistance of the combination will be $5\Omega$. Statement II : Two resistance $2R$ and $3R$ are connected in parallel in an electric circuit. The value of thermal energy developed in $3R$ and $2R$ will be in the ratio $3:2$. In the light of the above statements, choose the most appropriate answer from the options given below

Given below are two statements : Statement I: A time varying electric field is a source of changing magnetic field and vice-versa. Thus a disturbance in electric or magnetic field creates EM waves. Statement II: In a material medium, the EM wave travels with speed $v=\frac{1}{\sqrt{{\mu }_{0}{\epsilon }_{0}}}$. In the light of the above statements, choose the correct answer from the options given below.

Given below are two statements. Statement I : Electric potential is constant within and at the surface of each conductor. Statement II : Electric field just outside a charged conductor is perpendicular to the surface of the conductor at every point. In the light of the above statements, choose the most appropriate answer from the options give below.

Given below are two statements : Statement-I: The reactance of an ac circuit is zero. It is possible that the circuit contains a capacitor and an inductor. Statement-II: In ac circuit, the average power delivered by the source never becomes zero. In the light of the above statements, choose the correct answer from the options given below

Given below are two statements : Statement $I$: The electric force changes the speed of the charged particle and hence changes its kinetic energy; whereas the magnetic force does not change the kinetic energy of the charged particle. Statement $\mathrm{II}$: The electric force accelerates the positively charged particle perpendicular to the direction of electric field. The magnetic force accelerates the moving charged particle along the direction of magnetic field. In the light of the above statements, choose the most appropriate answer from the options given below :

Given below two statements : One is labelled as Assertion (A) and other is labelled as Reason (R). Assertion (A): Non-polar materials do not have any permanent dipole moment. Reason (R): When a non-polar material is placed in an electric field, the centre of the positive charge distribution of it's individual atom or molecule coincides with the centre of the negative charge distribution. In the light of above statements, choose the most appropriate answer from the options given below.

$27$ identical drops are charged at $22V$ each. They combine to form a bigger drop. The potential of the bigger drop will be _____ $V$.

Identify the correct statements from the following descriptions of various properties of electromagnetic waves. A. In a plane electromagnetic wave electric field and magnetic field must be perpendicular to each other and direction of propagation of wave should be along electric field or magnetic field. B. The energy in electromagnetic wave is divided equally between electric and magnetic fields. C. Both electric field and magnetic field are parallel to each other and perpendicular to the direction of propagation of wave. D. The electric field, magnetic field and direction of propagation of wave must be perpendicular to each other. E. The ratio of amplitude of magnetic field to the amplitude of electric field is equal to speed of light. Choose the most appropriate answer from the options given below:

If a charge $q$ is placed at the centre of a closed hemispherical non-conducting surface, the total flux passing through the flat surface would be 

If Electric field intensity of a uniform plane electro magnetic wave is given as $E=-301.6\mathrm{sin}(kz-\omega t){\hat{a}}_{x}+452.4\mathrm{sin}(kz-\omega t){\hat{a}}_{y}V{m}^{-1}.$ Then, magnetic intensity $H$ of this wave in $A{m}^{-1}$ will be [Given : Speed of light in vacuum $c=3\times {10}^{8}{ms}^{-1}$, Permeability of vacuum ${\mu }_{0}=4\pi \times {10}^{-7}N{A}^{-2}$]

If $n$ represents the actual number of deflections in a converted galvanometer of resistance $G$ and shunt resistance $S$. Then the total current $I$ when its figure of merit is $K$ will be

If the charge on a capacitor is increased by $2C$, the energy stored in it increases by $44%$. The original charge on the capacitor is (in $C$)

If the electric potential at any point $(x,y,z)m$ in space is given by $V=3{x}^{2}$ volt. The electric field at the point $(1,0,3)m$ will be :

If wattless current flows in the $\mathrm{AC}$ circuit, then the circuit is :

In a coil of resistance $8\Omega$, the magnetic flux due to an external magnetic field varies with time as $\phi =\frac{2}{3}(9-{t}^{2})$. The value of total heat produced in the coil, till the flux becomes zero, will be _____ $J$.

In a series $LR$ circuit ${X}_{L}=R$ and power factor of the circuit is ${P}_{1}$. When capacitor with capacitance $C$ such that ${X}_{L}={X}_{C}$ is put in series, the power factor becomes ${P}_{2}$. The ratio $\frac{{P}_{1}}{{P}_{2}}$ is

In a series LCR circuit, the inductance, capacitance and resistance are $L=100\mathrm{mH}$, $C=100\mu F$and $R=10\Omega$ respectively. They are connected to an $\mathrm{AC}$ source of voltage $220V$ and frequency of $50\mathrm{Hz}$. The approximate value of current in the circuit will be _____ $A$. 

In meter bridge experiment for measuring unknown resistance '$S$', the null point is obtained at a distance $30\mathrm{cm}$ from the left side as shown at point $D$. If $R$ is $5.6k\Omega$, then the value of unknown resistance '$S$' will be _____ $\Omega$. 

In the figure, a very large plane sheet of positive charge is shown. ${P}_{1}$ and ${P}_{2}$ are two points at distance $l$ and $2l$ from the charge distribution. If $\sigma$ is the surface charge density, then the magnitude of electric fields ${E}_{1}$ and ${E}_{2}$ at ${P}_{1}$ and ${P}_{2}$ respectively are 

In the given circuit 'a' is an arbitrary constant. The value of $m$ for which the equivalent circuit resistance is minimum, will be $\sqrt{\frac{x}{2}}$. The value of $x$ is _____ . 

In the given circuit, the magnitude of ${V}_{L}$ and ${V}_{C}$ are twice that of ${V}_{R}$. Given that $f=50\mathrm{Hz}$, the inductance of the coil is $\frac{1}{K\pi }\mathrm{mH}$. The value of $K$ is _____ . 

In the given figure of meter bridge experiment, the balancing length $AC$ corresponding to null deflection of the galvanometer is $40\mathrm{cm}$. The balancing length, if the radius of the wire $AB$ is doubled, will be _____ $\mathrm{cm}$. 

In the given figure, the value of ${V}_{0}$ will be _____ $V$. 

Light wave travelling in air along $x$-direction is given by ${E}_{y}=540\mathrm{sin}\pi \times {10}^{4}(x-ct)V{m}^{-1}$. Then, the peak value of magnetic field of wave will be (Given $c=3\times {10}^{8}m{s}^{-1}$)

The magnetic field at a distance r from a long straight wire carrying current I is:

Magnetic flux (in weber) in a closed circuit of resistance $20\Omega$ varies with time $t(s)$ as $\phi =8{t}^{2}-9t+5$. The magnitude of the induced current at $t=0.25s$ will be _____ $\mathrm{mA}$.

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>Ultravoilet rays</td><td>(i)</td><td>Study crystal structure</td></tr><tr><td>(b)</td><td>Microwaves</td><td>(ii)</td><td>Greenhouse effect</td></tr><tr><td>(c)</td><td>Infrared waves</td><td>(iii)</td><td>Sterilizing surgical instrument</td></tr><tr><td>(d)</td><td>$X$-rays</td><td>(iv)</td><td>Radar system</td></tr></tbody></table>

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>AC generator</td><td>(I)</td><td>Detects the presence of current in the circuit</td></tr><tr><td>(B)</td><td>Galvanometer</td><td>(II)</td><td>Converts mechanical energy into electrical energy</td></tr><tr><td>(C)</td><td>Transformer</td><td>(III)</td><td>Works on the principle of resonance in AC circuit</td></tr><tr><td>(D)</td><td>Metal detector</td><td>(IV)</td><td>Changes an alternating voltage for smaller or greater value</td></tr></tbody></table>

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>UV rays</td><td>(i)</td><td>Diagnostic tool in medicine</td></tr><tr><td>(b)</td><td>$X$-rays</td><td>(ii)</td><td>Water purification</td></tr><tr><td>(c)</td><td>Microwave</td><td>(iii)</td><td>Communication, Radar</td></tr><tr><td>(d)</td><td>Infrared wave</td><td>(iv)</td><td>Improving visibility in foggy days</td></tr></tbody></table>Choose the correct answer from the options given below :

Resistance are connected in a meter bridge circuit as shown in the figure. The balancing length ${l}_{1}$ is $40\mathrm{cm}$. Now an unknown resistance $x$ is connected in series with $P$ and new balancing length is found to be $80\mathrm{cm}$ measured from the same end. Then the value of $x$ will be _____ $\Omega$. 

Sixty four conducting drops each of radius $0.02m$ and each carrying a charge of $5\mu C$ are combined to form a bigger drop. The ratio of surface density of bigger drop to the smaller drop will be

Statement-I : A point charge is brought in an electric field. The value of electric field at a point near to the charge may increase if the charge is positive. Statement-II : An electric dipole is placed in a uniform electric field. The net electric force on the dipole will not be zero.

Sun light falls normally on a surface of area $36{\mathrm{cm}}^{2}$ and exerts an average force of $7.2\times {10}^{-9}N$ within a time period of $20$ minutes. Considering a case of complete absorption, the energy flux of incident light is

The charge on capacitor of capacitance $15\mu F$ in the figure given below is 

The combination of two identical cells, whether connected in series or parallel combination provides the same current through an external resistance of $2\Omega$. The value of internal resistance of each cell is

The current density in a cylindrical wire of radius $4\mathrm{mm}$ is $4\times {10}^{6}A{m}^{-2}$. The current through the outer portion of the wire between radial distances $\frac{R}{2}$ and $R$ is _____ $\pi A$.

The current density in a cylindrical wire of radius $r=4.0\mathrm{mm}$ is $1.0\times {10}^{6}{A}^{2}{m}^{2}$. The current through the outer portion of the wire between radial distances $\frac{r}{2}$ and $r$ is $x\pi A$; where $x$ is

The current flowing through an ac circuit is given by $I=5\mathrm{sin}(120\pi t)A$. How long will the current take to reach the peak value starting from zero?

The current I flowing through the given circuit will be _____ $A$. 

The current in a coil of self inductance $L=2.0H$ is increasing according to the law $i=2\mathrm{sin}({t}^{2})$. Find the amount of energy spent (in $J$) during the period when the current changes from $0$ to $2A$.

The current $I$ in the given circuit will be 

The current sensitivity of a galvanometer can be increased by : (A) decreasing the number of turns (B) increasing the magnetic field (C) decreasing the area of the coil (D) decreasing the torsional constant of the spring Choose the most appropriate answer from the options given below :

The displacement current of $4.425\mu A$ is developed in the space between the plates of parallel plate capacitor when voltage is changing at a rate of ${10}^{6}V{s}^{-1}$. The area of each plate of the capacitor is $40{\mathrm{cm}}^{2}$. The distance between each plate of the capacitor is $x\times {10}^{-3}m$. The value of $x$ is , (Permittivity of free space, ${\epsilon }_{0}=8.85\times {10}^{-12}{C}^{2}{N}^{-1}{m}^{-2}$) _______

The effective current $I$ in the given circuit at very high frequencies will be _____ $A$. 

The electric current in a circular coil of $2$ turns produces a magnetic induction ${B}_{1}$ at its centre. The coil is unwound and is rewound into a circular coil of $5$ turns and the same current produces a magnetic induction ${B}_{2}$ at its centre. The ratio of $\frac{{B}_{2}}{{B}_{1}}$ is:

The electric field in an electromagnetic wave is given by $E=56.5\mathrm{sin}\omega (\frac{t-x}{c}){\mathrm{NC}}^{-1}$. Find the intensity of the wave if it is propagating along $x$-axis in the free space. (Given ${\epsilon }_{0}=8.85\times {10}^{-12}{C}^{2}{N}^{-1}{m}^{-2}$)

The electromagnetic waves travel in a medium at a speed of $2.0\times {10}^{8}m{s}^{-1}$. The relative permeability of the medium is $1.0$. The relative permittivity of the medium will be

The equation of current in a purely inductive circuit is $5\mathrm{sin}(49\pi t-30^{\circ})$. If the inductance is $30\mathrm{mH}$ then the equation for the voltage across the inductor, will be

The equivalent capacitance between points $A$ and $B$ in below shown figure will be _____ $\mu F$. 

The frequencies at which the current amplitude in an LCR series circuit becomes $\frac{1}{\sqrt{2}}$ times its maximum value, are $212\mathrm{rad}{s}^{-1}$ and $232\mathrm{rad}{s}^{-1}$. The value of resistance in the circuit is $R=5\Omega$. The self inductance in the circuit is _____ $\mathrm{mH}$.

The intensity of the light from a bulb incident on a surface is $0.22W{m}^{-2}$. The amplitude of the magnetic field in this light-wave is _____ $\times {10}^{-9}T$ (Given : Permittivity of vacuum ${\epsilon }_{0}=8.85\times {10}^{-12}{C}^{2}{N}^{-1}{m}^{-2}$, speed of light in vacuum $c=3\times {10}^{8}{ms}^{-1}$)

The length of a given cylindrical wire is increased to double of its original length. The percentage increase in the resistance of the wire will be _____ $%$

The magnetic field at the center of current carrying circular loop is ${B}_{1}$. The magnetic field at a distance of $\sqrt{3}$ times radius of the given circular loop from the center on its axis is ${B}_{2}$. The value of $\frac{{B}_{1}}{{B}_{2}}$ will be

The magnetic field at the centre of a circular coil of radius $r$, due to current I flowing through it, is $B$. The magnetic field at a point along the axis at a distance $\frac{r}{2}$ from the centre is :

The magnetic field of a plane electromagnetic wave is given by $\vec{B}=2\times {10}^{-8}\mathrm{sin}(0.5\times {10}^{3}x+1.5\times {10}^{11}t)\hat{j}T$. The amplitude of the electric field would be

The magnetic flux through a coil perpendicular to its plane is varying according to the relation $\phi =(5{t}^{3}+4{t}^{2}+2t-5)$ Weber. If the resistance of the coil is $5\mathrm{ohm}$, then the induced current through the coil at $t=2s$ will be,

The magnetic moment of an electron $(e)$ revolving in an orbit around nucleus with an orbital angular momentum is given by

The oscillating magnetic field in a plane electromagnetic wave is given by ${B}_{y}=5\times {10}^{-6}\mathrm{sin}1000\pi (5x-4\times {10}^{8}t)T$. The amplitude of electric field will be

The RMS value of conduction current in a parallel plate capacitor is $6.9\mu A$. The capacity of this capacitor, if it is connected to $230V$ AC supply with an angular frequency of $600\mathrm{rad}{s}^{-1}$, will be

The soft-iron is a suitable material for making an electromagnet. This is because soft-iron has

The susceptibility of a paramagnetic material is $99$. The permeability of the material in $\mathrm{Wb}/A-m$, is [Permeability of free space ${\mu }_{0}=4\pi \times {10}^{-7}\mathrm{Wb}/A-m$]

The three charges $\frac{q}{2},q$ and $\frac{q}{2}$ are placed at the corners $A,D$ and $C$ of a square of side $a$ as shown in figure. The magnitude of electric field $(E)$ at the corner $B$ of the square, is 

The total charge on the system of capacitance ${C}_{1}=1\mu F,{C}_{2}=2\mu F,{C}_{3}=4\mu F$ and ${C}_{4}=3\mu F$ connected in parallel is (Assume a battery of $20V$ is connected to the combination)

The total current supplied to the circuit as shown in figure by the $5V$ battery is _____ $A$. 

The variation of applied potential and current flowing through a given wire is shown in figure. The length of wire is $31.4\mathrm{cm}$. The diameter of wire is measured as $2.4\mathrm{cm}$. The resistivity of the given wire is measured as $x\times {10}^{-3}\Omega \mathrm{cm}$. The value of $x$ is _____ . [Take $\pi =3.14$] 

The volume charge density of a sphere of radius $6m$ is $2\mu C{\mathrm{cm}}^{-3}$. The number of lines of force per unit surface area coming out from the surface of the sphere is _____ $\times {10}^{10}N{C}^{-1}.$ [Given : Permittivity of vacuum ${\epsilon }_{0}=8.85\times {10}^{-12}{C}^{2}{N}^{-1}-{m}^{-2}$]

Three identical charged balls each of charge $2C$ are suspended from a common point $P$ by silk threads of $2m$ each (as shown in figure). They form an equilateral triangle of side $1m$. The ratio of net force on a charged ball to the force between any two charged balls will be 

Three point charges of magnitude $5\mu C,0.16\mu C$ and $0.3\mu C$ are located at the vertices $A,B,C$ of a right angled triangle whose sides are $AB=3\mathrm{cm}$, $BC=3\sqrt{2}\mathrm{cm}$ and $CA=3\mathrm{cm}$ and point $A$ is the right angle corner. Charge at point $A$ experiences _____ $N$ of electrostatic force due to the other two charges.

To increase the resonant frequency in series LCR circuit,

To light, a $50W,100V$ lamp is connected, in series with a capacitor of capacitance $\frac{50}{\pi \sqrt{x}}\mu F$, with $200V,50\mathrm{Hz}\mathrm{AC}$ source. The value of $x$ will be _____ .

Two bar magnets oscillate in a horizontal plane in earth's magnetic field with time periods of $3s$ and $4s$respectively. If their moments of inertia are in the ratio of $3:2$ then the ratio of their magnetic moments will be

Two capacitors, each having capacitance $40\mu F$ are connected in series. The space between one of the capacitors is filled with dielectric material of dielectric constant $K$ such that the equivalence capacitance of the system became $24\mu F$. The value of $K$ will be :

Two capacitors having capacitance ${C}_{1}$ and ${C}_{2}$ respectively are connected as shown in figure. Initially, capacitor ${C}_{1}$ is charged to a potential difference $V$ volt by a battery. The battery is then removed and the charged capacitor ${C}_{1}$ is now connected to uncharged capacitor ${C}_{2}$ by closing the switch $S$. The amount of charge on the capacitor ${C}_{2}$, after equilibrium, is 

Two cells of the same EMF $E$ but different internal resistances ${r}_{1}$ and ${r}_{2}$ are connected in series with an external resistance $R$ as shown in the figure. The terminal potential difference across, the second cell is found to be zero. The external resistance $R$ must then be: 

Two charged particles, having same kinetic energy, are allowed to pass through a uniform magnetic field perpendicular to the direction of motion. If the ratio of radii of their circular paths is $6:5$ and their respective masses ratio is $9:4$. Then, the ratio of their charges will be

Two coils of self inductance ${L}_{1}$ and ${L}_{2}$ are connected in series combination having mutual inductance of the coils as $M$. The equivalent self inductance of the combination will be 

Two coils require $20$ minutes and $60$ minutes respectively to produce same amount of heat energy when connected separately to the same source. If they are connected in parallel arrangement to the same source; the time required to produce same amount of heat by the combination of coils, will be _____ $\mathrm{min}$.

Two concentric circular loops of radii ${r}_{1}=30\mathrm{cm}$ and ${r}_{2}=50\mathrm{cm}$ are placed in $X-Y$ plane as shown in the figure. A current $I=7A$ is flowing through them in the direction as shown in figure. The net magnetic moment of this system of two circular loops is approximately 

Two electric dipoles of dipole moments $1.2\times {10}^{-30}\mathrm{cm}$ and $2.4\times {10}^{-30}\mathrm{cm}$ are placed in two difference uniform electric fields of strengths $5\times {10}^{4}N{C}^{-1}$ and $15\times {10}^{4}N{C}^{-1}$ respectively. The ratio of maximum torque experienced by the electric dipoles will be $\frac{1}{x}$. The value of $x$ is _____ .

Two identical cells each of emf $1.5V$ are connected in parallel across a parallel combination of two resistors each of resistance $20\Omega$. A voltmeter connected in the circuit measures $1.2V$. The internal resistance of each cell is :

Two identical charged particles each having a mass $10g$ and charge $2.0\times {10}^{-7}C$ are placed on a horizontal table with a separation of $L$ between them such that they stay in limited equilibrium. If the coefficient of friction between each particle and the table is $0.25$, find the value of $L$. [Use $g=10{\mathrm{ms}}^{-2}$ ]

Two identical metallic spheres $A$ and $B$ when placed at certain distance in air repel each other with a force of $F$. Another identical uncharged sphere $C$ is first placed in contact with $A$ and then in contact with $B$ and finally placed at midpoint between spheres $A$and $B$. The force experienced by sphere $C$ will be :

Two identical positive charges $Q$ each are fixed at a distance of $2a$ apart from each other. Another point charge ${q}_{0}$ with mass $m$ is placed at midpoint between two fixed charges. For a small displacement along the line joining the fixed charges, the charge ${q}_{0}$ executes SHM. The time period of oscillation of charge ${q}_{0}$ will be

Two identical thin metal plates has charge ${q}_{1}$ and ${q}_{2}$ respectively such that ${q}_{1}>{q}_{2}$. The plates were brought close to each other to form a parallel plate capacitor of capacitance $C$. The potential difference between them is :

Two long current carrying conductors are placed parallel to each other at a distance of $8\mathrm{cm}$ between them. The magnitude of magnetic field produced at mid-point between the two conductors due to current flowing in them is $300\mu T$. The equal current flowing in the two conductors is :

Two long parallel conductors ${S}_{1}$ and ${S}_{2}$ are separated by a distance $10\mathrm{cm}$ and carrying currents of $4A$ and $2A$ respectively. The conductors are placed along $x$-axis in $X-Y$ plane. There is a point $P$ located between the conductors (as shown in figure). A charge particle of $3\pi$ coulomb is passing through the point $P$ with velocity $\vec{v}=(2\hat{i}+3\hat{j})m{s}^{-1}$; where $\hat{i}$ & $\hat{j}$ represents unit vector along $x$ & $y$axis respectively. The force acting on the charge particle is $4\pi \times {10}^{-5}(-x\hat{i}+2\hat{j})N$. The value of $x$ is 

Two $10\mathrm{cm}$ long, straight wires, each carrying a current of $5A$ are kept parallel to each other. If each wire experienced a force of ${10}^{-5}N$, then separation between the wires is _____ $\mathrm{cm}.$

Two metallic plates form a parallel plate capacitor. The distance between the plate is '$d$'. A metal sheet of thickness $\frac{d}{2}$ and of area equal to area of each plate is introduced between the plates. What will be the ratio of the new capacitance to the original capacitance of the capacitor?

Two parallel, long wires are kept $0.20m$ apart in vacuum, each carrying current of $xA$ in the same direction. If the force of attraction per meter of each wire is $2\times {10}^{-6}N$, then the value of $x$ is approximately

Two parallel plate capacitors of capacity $C$ and $3C$ are connected in parallel combination and charged to a potential difference $18V$. The battery is then disconnected and the space between the plates of the capacitor of capacity $C$ is completely filled with a material of dielectric constant $9$. The final potential difference across the combination of capacitors will be _____ $V$.

Two point charges $A$ and $B$ of magnitude $+8\times {10}^{-6}C$ and $-8\times {10}^{-6}C$ respectively are placed at a distance $d$ apart. The electric field at the middle point $O$ between the charges is $6.4\times {10}^{4}N{C}^{-1}$. The distance '$d$' between the point charges $A$ and $B$ is

Two point charges $Q$ each are placed at a distance $d$ apart. A third point charge $q$ is placed at a distance $x$ from mid-point on the perpendicular bisector. The value of $x$ at which charge $q$ will experience the maximum Coulomb's force is:

Two resistors are connected in series across a battery as shown in figure. If a voltmeter of resistance $2000\Omega$ is used to measure the potential difference across $500\Omega$ resister, the reading of the voltmeter will be _____ $V$ 

Two sources of equal emfs are connected in series. This combination is connected to an external resistance $R$. The internal resistances of the two sources are ${r}_{1}$ and ${r}_{2}({r}_{1}>{r}_{2})$. If the potential difference across the source of internal resistance ${r}_{1}$ is zero then the value of $R$ will be

Two uniformly charged spherical conductors $A$ and $B$ of radii $5\mathrm{mm}$ and $10\mathrm{mm}$ are separated by a distance of $2\mathrm{cm}$. If the spheres are connected by a conducting wire, then in equilibrium condition, the ratio of the magnitudes of the electric fields at the surface of the sphere $A$ and $B$ will be

What will be the most suitable combination of three resistors $A=2\Omega ,B=4\Omega ,C=6\Omega$ so that $(\frac{22}{3})\Omega$ is equivalent resistance of combination?

When you walk through a metal detector carrying a metal object in your pocket, it raises an alarm. This phenomenon works on

Which is the correct ascending order of wavelengths?