JEE Main Physics — Electromagnetism previous year questions with solutions.
Two charged conducting spheres $S_1$ and $S_2$ of radii $8$ cm and $18$ cm are connected to each other by a wire. After equilibrium is established, the ratio of electric fields on $S_1$ and $S_2$ spheres are $E_{S_1}$ and $E_{S_2}$ respectively. The value of $\dfrac{E_{S_1}}{E_{S_2}}$ is _______.
A point charge $q=1 \mu \mathrm{C}$ is located at a distance 2 cm from one end of a thin insulating wire of length 10 cm having a charge $Q=24 \mu \mathrm{C}$, distributed uniformly along its length, as shown in figure. Force between $q$ and wire is $\_\_\_\_$ N. (Use : $\frac{1}{4 \pi \epsilon_{\mathrm{o}}}=9 \times 10^{9} \mathrm{~N}. \mathrm{m}^{2} / \mathrm{C}^{2}$) 
Figure shows the circuit that contains three resistances ($9 \Omega$ each) and two inductors (4 mH each). The reading of ammeter at the moment switch $K$ is turned ON, is $\_\_\_\_$ A. 
A parallel plate capacitor with plate separation 5 mm is charged by a battery. On introducing a mica sheet of 2 mm and maintaining the connections of the plates with the terminals of the battery, it is found that it draws $25 \%$ more charge from the battery. The dielectric constant of mica is $\_\_\_\_$.
The charged particle moving in a uniform magnetic field of $(3\hat{i} + 2\hat{j})$ T has an acceleration $\left(4\hat{i} - \dfrac{x}{2}\hat{j}\right)$ m/s$^2$. The value of $x$ is __________.
Match the LIST-I with LIST-II \(\begin{array}{|l|l|l|l|} \hline & \text{List-I} & & \text{List-II} \\ \hline \text{A.} & \text{Radio-wave} & \text{I.} & \text{is produced by Magnetron valve} \\ \hline \text{B.} & \text{Micro-wave} & \text{II.} & \text{due to change in the vibrational modes of atoms} \\ \hline \text{C.} & \text{Infrared-wave} & \text{III.} & \text{due to inner shell electrons moving from higher to lower energy level} \\ \hline \text{D.} & \text{X-ray} & \text{IV.} & \text{due to rapid acceleration of electrons} \\ \hline \end{array}\) Choose the correct answer from the options given below:
A series LCR circuit with $R = 20\ \Omega$, $L = 1.6\text{ H}$ and $C = 40\ \mu\text{F}$ is connected to a variable frequency a.c. source. The inductive reactance at resonant frequency is _______ $\Omega$.
A three coulomb charge moves from the point $(0, -2, -5)$ to the point $(5, 1, 2)$ in an electric field expressed as $\vec{E} = 2x\hat{i} + 3y^2\hat{j} + 4\hat{k}$ N/C. The work done in moving the charge is _______ J.
An a.c. source of angular frequency $\omega$ is connected across a resistor $R$ and a capacitor $C$ in series. The current is observed as $I$. Now the frequency of the source is changed to $\omega/4$, (keeping the voltage unchanged) the current is found to be $I/3$. The ratio of resistance to reactance at frequency $\omega$ is
A simple pendulum made of mass 10 g and a metallic wire of length 10 cm is suspended vertically in a uniform magnetic field of 2 T. The magnetic field direction is perpendicular to the plane of oscillations of the pendulum. If the pendulum is released from an angle of $60^{\circ}$ with vertical, then maximum induced EMF between the point of suspension and point of oscillation is $\_\_\_\_$ mV. (Take $\mathrm{g}=10 \mathrm{~m} / \mathrm{s}^{2}$)
A capacitor $C$ is first charged fully with potential difference of $V_{0}$ and disconnected from the battery. The charged capacitor is connected across an inductor having inductance $L$. In $t \mathrm{~s} \ 25 \%$ of the initial energy in the capacitor is transferred to the inductor. The value of $t$ is $\_\_\_\_$ s.
Two short electric dipoles $A$ and $B$ having dipole moment $p_1$ and $p_2$ respectively are placed with their axis mutually perpendicular as shown in the figure. The resultant electric field at a point $x$ is making an angle of $60°$ with the line joining points $O$ and $x$. The ratio of the dipole moments $p_2/p_1$ is _______. 
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Consider a ferromagnetic material : Assertion (A) : The individual atoms in a ferromagnetic material possess a magnetic dipole moment and interact with one another in such a way that they spontaneously align themselves forming domains. Reason (R): At high enough temperature, the domain structure of ferromagnetic material disintegrates. Thus, magnetization will disappear at high enough temperature known as Curie temperature. In the light of the above statements, choose the correct answer from the options given below :
Inductance of a coil with $10^{4}$ turns is 10 mH and it is connected to a dc source of 10 V with internal resistance of $10 \Omega$. The energy density in the inductor when the current reaches $\left(\frac{1}{e}\right)$ of its maximum value is $\alpha \pi \times \frac{1}{e^{2}} \mathrm{~J} / \mathrm{m}^{3}$. The value of $\alpha$ is $\_\_\_\_$. ($\mu_{0}=4 \pi \times 10^{-7} \mathrm{Tm} / \mathrm{A}$).
For the series $L C R$ circuit connected with $220 \mathrm{~V}, 50 \mathrm{~Hz}$ a.c source as shown in the figure, the power factor is $\frac{\alpha}{10}$. The value of $\alpha$ is $\_\_\_\_$. 
Identify the correct statements : A. Effective capacitance of a series combination of capacitors is always smaller than the smallest capacitance of the capacitor in the combination. B. When a dielectric medium is placed between the charged plates of a capacitor, displacement of charges cannot occur due to insulation property of dielectric. C. Increasing of area of capacitor plate or decreasing of thickness of dielectric is an alternate method to increase the capacitance. D. For a point charge, concentric spherical shells centered at the location of the charge are equipotential surfaces. Choose the correct answer from the options given below :
 Two identical circular loops $P$ and $Q$ each of radius $r$ are lying in parallel planes such that they have common axis. The current through $P$ and $Q$ are $I$ and $4 I$ respectively in clockwise direction as seen from $O$. The net magnetic field at $O$ is:
A 20 m long uniform copper wire held horizontally is allowed to fall under the gravity ($g=10 \mathrm{~m} / \mathrm{s}^{2}$) through a uniform horizontal magnetic field of 0.5 Gauss perpendicular to the length of the wire. The induced EMF across the wire when it travells a vertical distance of 200 m is $\_\_\_\_$ mV.
Match List - I with List - II. $\begin{array}{l} \text{List - I} & \text{List - II} \\ \text{Relation} & \text{Law} \\ \text{A. } \oint \vec{E} \cdot \overrightarrow{d l}=-\frac{d}{d t} \oint \vec{B} \cdot \overrightarrow{d a} & \text{I. Ampere's circuital law} \\ \text{B. } \oint \vec{B} \cdot \overrightarrow{d l}=\mu_{0}\left(I+\epsilon_{0} \frac{d \phi_{E}}{d t}\right) & \text{II. Faraday's laws of} \\ & \text{electromagnetic induction} \\ \text{C. } \oint \vec{E} \cdot \overrightarrow{d a}=\frac{1}{\epsilon_{0}} \int_{\mathrm{V}} \rho \mathrm{dv} & \text{III. Ampere - Maxwell law} \\ \text{D. } \oint \vec{B} \cdot \overrightarrow{d l}=\mu_{0} I & \text{IV. Gauss's law of electrostatics} \end{array}$ Choose the correct answer from the options given below :
A sphere of capacitance $100$ pF is charged to a potential of $100$ V. Another identical uncharged metal sphere is brought in contact with the charged sphere, then the change in the total energy stored on these spheres, when they touch is $\alpha \times 10^{-7}$ J. The value of $\alpha$ is __________. (combined capacitance of spheres is $200$ pF)
Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R Assertion A: In electrostatics, a conductor does not store any net charge inside. Reason R: Inside the capacitor (with no dielectric medium), the free charge carriers, if placed between the plates of capacitor, experience force and drift. Choose the correct answer from the options given below
An inductor of inductance $10$ mH having resistance of $100\,\Omega$ is connected to battery of E.M.F. $1.0$ V through a switch as shown in the figure below. After switch is closed, the ratio of instantaneous voltages across the inductor when the current passing through it is $2$ mA and $4$ mA is _______. 
Two shorts dipoles $(A, B), A$ having charges $\pm 2 \mu \mathrm{C}$ and length 1 cm and $B$ having charges $\pm 4 \mu \mathrm{C}$ and length 1 cm are placed with their centres 80 cm apart as shown in the figure. The electric field at a point $P$, equi-distant from the centres of both dipoles is $\_\_\_\_$ N/C. 
The electric field of a plane electromagnetic wave, travelling in an unknown nonmagnetic medium is given by, $E_{\mathrm{y}}=20 \sin \left(3 \times 10^{6} x-4.5 \times 10^{14} \mathrm{t}\right) \mathrm{V} / \mathrm{m}$ (where $x, \mathrm{t}$ and other values have S.I. units). The dielectric constant of the medium is $\_\_\_\_$ (speed of light in free space is $3 \times 10^{8} \mathrm{~m} / \mathrm{s}$)