JEE Main Physics — Electromagnetism previous year questions with solutions.
An electric bulb rated as $200W$ at $100V$ is used in a circuit having $200V$ supply. The resistance $R$ that must be put in series with the bulb so that the bulb delivers the same power is ______ $\Omega$.
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 $\frac{22}{7}]$
Consider an electrical circuit containing a two way switch $S.$ Initially $S$ is open and then ${T}_{1}$ is connected to ${T}_{2}.$ As the current in $R=6\Omega$ attains a maximum value of steady-state level, ${T}_{1}$ is disconnected from ${T}_{2}$ and immediately connected to ${T}_{3}.$ Potential drop across $r=3\Omega$ resistor immediately after ${T}_{1}$ is connected to ${T}_{3}$ is $______V.$ (Round off to the Nearest Integer) 
A transmitting station releases waves of wavelength $960m$. A capacitor of $2.56\mu F$ is used in the resonant circuit. The self-inductance of coil necessary for resonance is $x\times {10}^{-8}H$. find $x$
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 sinusoidal voltage of peak value $250V$ is applied to a series $LCR$ circuit, in which $R=8\Omega ,L=24\mathrm{mH}$ and $C=60\mu F$. The value of power dissipated at resonant condition is $x$ $\mathrm{kW}$. The value of $x$ to the nearest integer is _______.
A small square loop of side $a$ and one turn is placed inside a larger square loop of side $b$ and one turn $(b\gg a).$ The two loops are coplanar with their centres coinciding. If a current $I$ is passed in the square loop of side $b,$ then the coefficient of mutual inductance between the two loops is :
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 _________.
The magnetic field vector of an electromagnetic wave is given by $B={B}_{0}\frac{\hat{i}+\hat{j}}{\sqrt{2}}\mathrm{cos}(kz-\omega t)$ where $\hat{i},\hat{j}$ represents unit vector along $x$ and $y$-axis respectively. At $t=0s,$ two electric charges ${q}_{1}$ of $4\pi$ coulomb and ${q}_{2}$ of $2\pi$ coulomb located at $(0,0,\frac{\pi }{k})$ and $(0,0,\frac{3\pi }{k}),$ respectively, have the same velocity of $0.5c\hat{i},$ (where $c$ is the velocity of light ). The ratio of the force acting on charge ${q}_{1}$ to ${q}_{2}$ is :
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 ______.
The arm $PQ$ of a rectangular conductor is moving from $x=0$ to $x=2b$ outwards and then inwards from $x=2b$ to $x=0$ as shown in the figure. A uniform magnetic field perpendicular to the plane is acting from $x=0$ to $x=b.$ Identify the graph showing the variation of different quantities with distance:  
A coil is placed in a magnetic field $\vec{B}$ as shown below :  A current is induced in the coil because $\vec{B}$ is :
Magnetic fields at two points on the axis of a circular coil at a distance of $0.05m$ and $0.2m$ from the centre are in the ratio $8:1$. The radius of coil is _______ .
Figure shows a rod $AB$, which is bent in a $120^{\circ}$ circular arc of radius $R$. A charge$(-Q)$ is uniformly distributed over rod $\mathrm{AB}$. What is the electric filed $\vec{E}$ at the centre of curvature $O$ ? 
A solid metal sphere of radius $R$ having charge $q$ is enclosed inside the concentric spherical shell of inner radius $a$ and outer radius $b$ as shown in the figure. The approximate variation electric field $\vec{E}$, as a function of distance $r$, from centre $O$, is given by: 
Two small spheres each of mass $10\mathrm{mg}$ are suspended from a point by threads $0.5m$ long. They are equally charged and repel each other to a distance of $0.20m$. The charge on each of the sphere is $\frac{a}{21}\times {10}^{-8}C.$ The value of $a$ will be ___.[Given $g=10m{s}^{-2}$]
The total charge enclosed in an incremental volume of $2\times {10}^{-9}{m}^{3}$ located at the origin is $\mathrm{nC},$ if electric flux density of its field is found as$D={e}^{-x}\mathrm{sin}y\hat{i}-{e}^{-x}\mathrm{cosy}\hat{j}+2z\hat{k}C{m}^{-2}$
The electric field intensity is produced by the radiation coming from a $100W$ bulb at a distance of $3m$ is $E$. The electric field intensity produced by the radiation coming from $60W$ at the same distance is $\sqrt{\frac{x}{5}}E$. Where the value of $x=$_________ .
An infinite number of point charges, each carrying $1\mu C$ charge, are placed along the y-axis at $y=1m,2m,4m,8m....$ The total force on a $1C$ point charge, placed at the origin, is $x\times {10}^{3}N$. The value of $x$, to the nearest integer, is ___ . [Take $\frac{1}{4\pi {\epsilon }_{0}}=9\times {10}^{9}N{m}^{2}{C}^{-2}$]
Given below are two statements Statement $I$ : An electric dipole is placed at the centre of a hollow sphere. The flux of electric field through the sphere is zero, but the electric field is not zero anywhere in the sphere. Statement $\mathrm{II}$ : If $R$ is the radius of a solid metallic sphere and $Q$ be the total charge on it. The electric field at any point on the spherical surface of radius $r(<R)$ is zero but the electric flux passing through this closed spherical surface of radius $r$ is not In the light of the above statements, choose the correct answer from the options given below:
A series LCR circuit of $R=5\Omega ,L=20\mathrm{mH}$ and $C=0.5\mu F$ is connected across an $\mathrm{AC}$ supply of $250V,$ having variable frequency. The power dissipated at resonance condition is ________$\times {10}^{2}W.$
A capacitor is connected to a $20V$ battery through a resistance of $10\Omega .$ It is found that the potential difference across the capacitor rises to $2V$ in $1\mu s.$ The capacitance of the capacitor is $________\mu F.$ Given In $(\frac{10}{9})=0.105$
Three capacitors ${C}_{1}=2\mu F,{C}_{2}=6\mu F$ and ${C}_{3}=12\mu F$ are connected as shown in the figure. Find the ratio of the charges on capacitors ${C}_{1},{C}_{2}$ and ${C}_{3}$ respectively. 
The material filled between the plates of a parallel plate capacitor has resistivity $200\Omega m$. The value of capacitance of the capacitor is $2\mathrm{pF}$. If a potential difference of $40V$ is applied across the plates of the capacitor, then the value of leakage current flowing out of the capacitor is: (given the value of relative permittivity of material is $50$)