JEE Main Physics — Electromagnetism previous year questions with solutions.
A conducting bar of length $L$ is free to slide on two parallel conducting rails as shown in the figure  Two resistors ${R}_{1}$ and ${R}_{2}$ are connected across the ends of the rails. There is a uniform magnetic field $\vec{B}$ pointing into the page. An external agent pulls the bar to the left at a constant speed $v$. The correct statement about the directions of induced currents ${I}_{1}$ and ${I}_{2}$ flowing through ${R}_{1}$ and ${R}_{2}$ respectively is :
A hairpin like shape as shown in figure is made by bending a long current carrying wire. What is the magnitude of a magnetic field at point $P$ which lies on the centre of the semicircle ? 
A cube of side $a$ has point charges $+Q$ located at each of its vertices except at the origin where the charge is $-Q.$ The electric field at the centre of cube is: 
If ${q}_{f}$ is the free charge on the capacitor plates and ${q}_{b}$ is the bound charge on the dielectric slab of dielectric constant $k$ placed between the capacitor plates, then bound charge ${q}_{b}$ can be expressed as :
For an electromagnetic wave travelling in free space, the relation between average energy densities due to electric $({U}_{e})$ and magnetic $({U}_{m})$ fields is :
A solenoid of $1000$ turns per metre has a core with relative permeability $500.$ Insulated windings of the solenoid carry an electric current of $5A.$ The magnetic flux density produced by the solenoid is: (Permeability of free space$=4\pi \times {10}^{-7}H{m}^{-1}$)
For the given circuit the current $i$ through the battery when the key in closed and the steady state has been reached is 
A plane electromagnetic wave of frequency $500\mathrm{MHz}$ is traveling in a vacuum along the $y-$direction. At a particular point in space and time, $\vec{B}=8.0\times {10}^{-8}\hat{z}T$. The value of the electric field at this point is:(speed of light $=3\times {10}^{8}{\mathrm{ms}}^{-1}$) $\hat{x},\hat{y},\hat{z}$ are unit vectors along $x,y$ and $z$ direction.
If $2.5\times {10}^{-6}N$ average force is exerted by a light wave on a non-reflecting surface of $30{\mathrm{cm}}^{2}$ area during $40\mathrm{min}$ of time span, the energy flux of light just before it falls on the surface is _______ $W{\mathrm{cm}}^{-2}.$(Round off to the Nearest Integer), (Assume complete absorption and normal incidence conditions are there)
For a series $\mathrm{LCR}$ circuit with $R=100\Omega ,L=0.5\mathrm{mH}$ and $C=0.1\mathrm{pF}$ connected across $220V-50\mathrm{Hz}$ $\mathrm{AC}$ supply, the phase angle between current and supplied voltage and the nature of the circuit is:
Two ions of masses $4\mathrm{amu}$ and $16\mathrm{amu}$ have charges $+2e$ and $+3e$ respectively. These ions pass through the region of the constant perpendicular magnetic field. The kinetic energy of both ions is the same. Then:
A charge $q$ is placed at one corner of a cube as shown in figure. The flux of electrostatic field $\vec{E}$ through the shaded area is: 
Five equal resistances are connected in a network as shown in figure. The net resistance between the points $A$ and $B$ is : 
An $L.C.R.$ circuit contains resistance of $110\Omega$ and a supply of $220V$ at $300\mathrm{rad}{s}^{-1}$ angular frequency. If only capacitance is removed from the circuit, current lags behind the voltage by $45^{\circ}$. If on the other hand, the only the inductor is removed the current leads by $45^{\circ}$ with the applied voltage. The $R.M.S.$ current flowing in the circuit will be:
The figure shows a circuit that contains four identical resistors with resistance $R=2.0\Omega ,$ two identical inductors with inductance $L=2.0\mathrm{mH}$ and an ideal battery with E.M.F. $E=9V.$ The current $i$ just after the switch $S$ is closed will be: 
First, a set of $n$ equal resistors of $10\Omega$ each are connected in series to a battery of E.M.F. $20V$ and internal resistance $10\Omega .$ A current $I$ is observed to flow. Then, the $n$ resistors are connected in parallel to the same battery. It is observed that the current is increased $20$ times, then the value of $n$ is ___________.
The relative permittivity of distilled water is $81.$ The velocity of light in it will be: $($Given ${\mu }_{r}=1)$
A particle of mass $1\mathrm{mg}$ and charge $q$ is lying at the mid-point of two stationary particles kept at a distance $2m$ when each is carrying same charge $q$. If the free charged particle is displaced from its equilibrium position through distance $x$ $(x<<1m)$. The particle executes SHM. Its angular frequency of oscillation will be _______ $\times {10}^{5}\mathrm{rad}{s}^{-1}$ (if ${q}^{2}=10{C}^{2}$)
The two thin coaxial rings, each of radius $a$ and having charges $+Q$ and $-Q$ respectively are separated by a distance of $s$. The potential difference between the centres of the two rings is :
A common transistor radio set requires $12V$ $(D.C.)$ for its operation. The $D.C.$ source is constructed by using a transformer and a rectifier circuit, which are operated at $220V$ $(A.C.)$ on standard domestic $A.C.$ supply. The number of turns of secondary coil are $24,$ then the number of turns of primary are
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>Phase difference between current and voltage in a purely resistive AC circuit</td><td>i</td><td>$\frac{\pi }{2};$ current leads voltage</td></tr><tr><td>b</td><td>Phase difference between current and voltage in a pure inductive AC circuit</td><td>ii</td><td>zero</td></tr><tr><td>c</td><td>Phase difference between current and voltage in a pure capacitive AC circuit</td><td>iii</td><td>$\frac{\pi }{2};$ current lags voltage</td></tr><tr><td>d</td><td>Phase difference between current and voltage in an LCR series circuit</td><td>iv</td><td>${\mathrm{tan}}^{-1}(\frac{{X}_{C}-{X}_{L}}{R})$</td></tr></tbody></table>Choose the most appropriate answer from the options given below :
A coil having $N$ turns is wound tightly in the form of a spiral with inner and outer radii $a$ and $b$ respectively. Find the magnetic field at centre, when a current $I$ passes through coil :
Two ions having same mass have charges in the ratio $1:2$. They are projected normally in a uniform magnetic field with their speeds in the ratio $2:3$. The ratio of the radii of their circular trajectories is,
A parallel-plate capacitor with plate area $A$ has separation $d$ between the plates. Two dielectric slabs of dielectric constant ${K}_{1}$ and ${K}_{2}$ of same area $\frac{A}{2}$ and thickness $\frac{d}{2}$ are inserted in the space between the plates. The capacitance of the capacitor will be given by : 