JEE Main Physics — Electromagnetism previous year questions with solutions.
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 ${q}^{2}=10{C}^{2}$)
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 : 
A parallel plate capacitor with plate area '$A$' and distance of separation '$d$' is filled with a dielectric. What is the capacity of the capacitor when permittivity of the dielectric varies as: $\epsilon (x)={\epsilon }_{0}+kx$, for $(0<x\leq \frac{d}{2})$ $\epsilon (x)={\epsilon }_{0}+k(d-x)$, for $(\frac{d}{2}\leq x\leq d)$
A parallel plate capacitor whose capacitance $C$ is $14\mathrm{pF}$ is charged by a battery to a potential difference $V=12V$ between its plates. The charging battery is now disconnected and a porcelain plate with $k=7$ is inserted between the plates, then the plate would oscillate back and forth between the plates with a constant mechanical energy of _______ $\mathrm{pJ}.$ (Assume no friction)
A parallel plate capacitor of capacitance $200\mu F$ is connected to a battery of $200V.$ A dielectric slab of dielectric constant $2$ is now inserted into the space between plates of capacitor while the battery remain connected. The change in the electrostatic energy in the capacitor will be __________ $J.$
A parallel plate capacitor has plate area $100{m}^{2}$ and plate separation of $10m.$ The space between the plates is filled up to a thickness $5m$ with a material of dielectric constant of $10.$ The resultant capacitance of the system is $x\mathrm{pF}.$ The value of ${\epsilon }_{0}=8.85\times {10}^{-12}F{m}^{-1}$. The value of $x$ to the nearest integer is ______.
A loop of flexible wire of irregular shape carrying current is placed in an external magnetic field. Identify the effect of the field on the wire.
A long solenoid with $1000\mathrm{turns}{m}^{-1}$ has a core material with relative permeability $500$ and volume ${10}^{3}{\mathrm{cm}}^{3}.$ If the core material is replaced by another material having relative permeability of $750$ with same volume maintaining same current of $0.75A$ in the solenoid, the fractional change in the magnetic moment of the core would be approximately $(\frac{x}{499}).$ Find the value of $x.$
A linearly polarised electromagnetic wave in vacuum is $E=3.1\mathrm{cos}[(1.8)z-(5.4\times {10}^{6})t]\hat{i}N{C}^{-1}$ is incident normally on a perfectly reflecting wall at $z=a$. Choose the correct option.
A light beam is described by $E=800\mathrm{sin}\omega (t-\frac{x}{c}).$ An electron is allowed to move normal to the propagation of light beam with a speed of $3\times {10}^{7}{ms}^{-1}$. What is the maximum magnetic force exerted on the electron?
A $0.07H$ inductor and a $12\Omega$ resistor are connected in series to a $220V,50\mathrm{Hz}$ AC source. The approximate current in the circuit and the phase angle between current and source voltage are respectively. [Take $\pi$ as $\frac{22}{7}]$
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 deuteron and an alpha particle having equal kinetic energy enter perpendicular into a magnetic field. Let ${r}_{d}$ and ${r}_{\alpha }$ be their respective radii of circular path. The value of $\frac{{r}_{d}}{{r}_{\alpha }}$ is equal to:
A cylindrical wire of radius $0.5\mathrm{mm}$ and conductivity $5\times {10}^{7}S{m}^{-1}$ is subjected to an electric field of $10\mathrm{mV}{m}^{-1}.$ The expected value of current in the wire will be ${x}^{3}\pi \mathrm{mA}.$ The value of $x$ is _________.
A current through a wire depends on time as $i={\alpha }_{0}t+\beta {t}^{2}$, where ${\alpha }_{0}=20A{s}^{-1}$ and $\beta =8A{s}^{-2}$. Find the charge crossed through a section of the wire in $15s.$
A current of $5A$ is passing through a non-linear magnesium wire of cross-section $0.04{m}^{2}$. At every point the direction of current density is at an angle of $60^{\circ}$ with the unit vector of area of cross-section. The magnitude of electric field at every point of the conductor is: (resistivity of magnesium $\rho =44\times {10}^{-8}\Omega m$)
A current of $1.5A$ is flowing through a triangle, of side $9\mathrm{cm}$ each. The magnetic field at the centroid of the triangle is : (Assume that the current is flowing in the clockwise direction.)
A current of $10A$ exists in a wire of cross-sectional area of $5{\mathrm{mm}}^{2}$ with a drift velocity of $2\times {10}^{-3}{ms}^{-1}.$ The number of free electrons in each cubic meter of the wire is
A current of $6A$ enters one corner $P$ of an equilateral triangle $PQR$ having $3$ wires of resistance $2\Omega$ each and leaves by the corner $R.$ The currents ${i}_{1}$ in ampere is 
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: 
A cube is placed inside an electric field, $\vec{E}=150{y}^{2}\hat{j}$ The side of the cube is $0.5m$ and is placed in the field as shown in the given figure. The charge inside the cube is: 
A Copper $(\mathrm{Cu})$ rod of length $25\mathrm{cm}$ and cross-sectional area $3{\mathrm{mm}}^{2}$ is joined with a similar Aluminium $(\mathrm{Al})$ rod as shown in figure. Find the resistance of the combination between the ends $A$ and $B.$ (Take resistivity of Copper $=1.7\times {10}^{-8}\Omega m$, Resistivity of aluminium $=2.6\times {10}^{-8}\Omega m$) 
A constant magnetic field of $1T$ is applied in the $x>0$ region. A metallic circular ring of radius $1m$ is moving with a constant velocity of $1m{s}^{-1}$ along the $x$-axis. At $t=0s$, the centre $O$ of the ring is at $x=-1m$. What will be the value of the induced emf in the ring at $t=1s$ ? (Assume the velocity of the ring does not change.) 
A conducting wire of length $l$, area of crosssection $A$ and electric resistivity $\rho$ is connected between the terminals of a battery. A potential difference $V$ is developed between its ends, causing an electric current. If the length of the wire of the same material is doubled and the area of cross-section is halved, the resultant current would be___