Electrostatics & Capacitors · JEE Main previous year questions

1. A.
2. B.
3. C.
4. D.

A parallel plate capacitor with plates of area $1{\mathrm{m}}^2$ each, are at a separation of 0.1 m. If the electric field between the plates is 100 N/C, the magnitude of charge on each plate is : (Take ${\epsilon }_0=8.85\times 10^{-12}\frac{C^2}{N\cdot m^2}$)

1. A.$9.85\times 10^{-10}\mathrm{C}$
2. B.$8.85\times 10^{-10}\mathrm{C}$
3. C.$6.85\times 10^{-10}\mathrm{C}$
4. D.$7.85\times 10^{-10}\mathrm{C}$

1. A.$\frac{6}{5}\mu F$
2. B.$\frac{7}{11}\mu F$
3. C.$4\mu \mathrm{F}$
4. D.$\frac{7}{10}\mu F$

1. A.zero
2. B.$1.5\mu \mathrm{A}$
3. C.$2\mu \mathrm{A}$
4. D.$3\mu \mathrm{A}$

An electric field of $1000\text{ V/m}$ is applied to an electric dipole at angle of $45^{\circ }$. The value of electric dipole moment is $10^{-29}\text{ C.m}$. What is the potential energy of the electric dipole?

1. A.$-7\times 10^{-27}\text{ J}$
2. B.$-9\times 10^{-20}\text{ J}$
3. C.$-10\times 10^{-29}\text{ J}$
4. D.$-20\times 10^{-18}\text{ J}$

A paramagnetic substance in the form of a cube with sides $1\text{ cm}$ has a magnetic dipole moment of $20\times 10^{-6}\text{ J/T}$ when a magnetic intensity of $60\times 10^3\text{ A/m}$ is applied. Its magnetic susceptibility is

1. A.$3.3\times 10^{-4}$
2. B.$2.3\times 10^{-2}$
3. C.$4.3\times 10^{-2}$
4. D.$3.3\times 10^{-2}$

A $27\text{ mW}$ laser beam has a cross-sectional area of $10{\text{ mm}}^2$. The magnitude of the maximum electric field in this electromagnetic wave is given by : [Given permittivity of space ${ϵ}_0=9\times 10^{-12}\text{ SI units}$, Speed of light $c=3\times 10^8\text{ m/s}$]

1. A.$2\text{ kV/m}$
2. B.$1\text{ kV/m}$
3. C.$1.4\text{ kV/m}$
4. D.$0.7\text{ kV/m}$

1. A.
2. B.
3. C.
4. D.

For a uniformly charged ring of radius R, the electric field on its axis has the largest magnitude at a distance h from its center. Then value of h is :

1. A.$\frac{R}{\sqrt{5}}$
2. B.$\frac{R}{\sqrt{2}}$
3. C.R
4. D.$R\sqrt{2}$

1. A.$\frac{K{ϵ}_0{a}^2}{2d(K+1)}$
2. B.$\frac{K{ϵ}_0{a}^2}{d(K-1)}\ln K$
3. C.$\frac{K{ϵ}_0{a}^2}{d}\ln K$
4. D.$\frac{1}{2}\frac{K{ϵ}_0{a}^2}{d}$

1. A.$C_{1}E[1-\exp (-tR/C_1)]$
2. B.$C_{2}E[1-\exp (-t/R{C}_2)]$
3. C.$C_{eq}E[1-\exp (-t/R{C}_{eq})]$
4. D.$C_{eq}E\exp (-t/R{C}_{eq})$

A body of mass $M$ and charge $q$ is connected to spring of spring constant $k$. It is oscillating along $x$-direction about its equilibrium position, taken to be at $x=0$, with an amplitude $A$. An electric field $E$ is applied along the $x$-direction. Which of the following statements is correct ?

1. A.The new equilibrium position is at a distance $\frac{qE}{2k}$ from $x=0$.
2. B.The total energy of the system is $\frac{1}{2}m{\omega }^2{A}^2+\frac{1}{2}\frac{q^2{E}^2}{k}$.
3. C.The total energy of the system is $\frac{1}{2}m{\omega }^2{A}^2-\frac{1}{2}\frac{q^2{E}^2}{k}$.
4. D.The new equilibrium position is at a distance $\frac{2qE}{k}$ from $x=0$.

1. A.$\frac{Q}{{ϵ}_0}$
2. B.$\frac{Q}{2{ϵ}_0}$
3. C.$\frac{Q}{3{ϵ}_0}$
4. D.$\frac{Q}{6{ϵ}_0}$

An ideal capacitor of capacitance $0.2\mu F$ is charged to a potential difference of $10V$. The charging battery is then disconnected. The capacitor is then connected to an ideal inductor of self inductance $0.5mH$. The current at a time when the potential difference across the capacitor is $5V$, is :

1. A.$0.34A$
2. B.$0.25A$
3. C.$0.17A$
4. D.$0.15A$

1. A.$2.4\mu F$
2. B.$4.9\mu F$
3. C.$3.6\mu F$
4. D.$5.4\mu F$

Three concentric metal shells A, B and C of respective radii a, b and c $(a<b<c)$ have surface charge densities $+\sigma ,-\sigma$ and $+\sigma$ respectively. The potential of shell B is :

1. A.$\frac{\sigma }{{ϵ}_0}\left[\frac{b^2-c^2}{c}+a\right]$
2. B.$\frac{\sigma }{{ϵ}_0}\left[\frac{a^2-b^2}{a}+c\right]$
3. C.$\frac{\sigma }{{ϵ}_0}\left[\frac{a^2-b^2}{b}+c\right]$
4. D.$\frac{\sigma }{{ϵ}_0}\left[\frac{b^2-c^2}{b}+a\right]$

A parallel plate capacitor of capacitance 90 pF is connected to a battery of emf 20 V. If a dielectric material of dielectric constant K = 5/3 is inserted between the plates, the magnitude of the induced charge will be :

1. A.0.9 n C
2. B.1.2 n C
3. C.0.3 n C
4. D.2.4 n C

The dipole moment of a circular loop carrying a current I, is m and the magnetic field at the centre of the loop is $B_1$. When the dipole moment is doubled by keeping the current constant, the magnetic field at the centre of the loop is $B_2$. The ratio $\frac{B_1}{B_2}$ is:

1. A.2
2. B.$\sqrt{3}$
3. C.$\sqrt{2}$
4. D.$\frac{1}{\sqrt{2}}$

An EM wave from air enters a medium. The electric fields are ${\vec{E}}_1=E_{01}\hat{x}\cos \left[2\pi \nu \left(\frac{z}{c}-t\right)\right]$ in air and ${\vec{E}}_2=E_{02}\hat{x}\cos [k(2z-ct)]$ in medium, where the wave number k and frequency $\nu$ refer to their values in air. The medium is non-magnetic. If ${\epsilon }_{r_1}$ and ${\epsilon }_{r_2}$ refer to relative permittivities of air and medium respectively, which of the following options is correct ?

1. A.$\frac{{\epsilon }_{r_1}}{{\epsilon }_{r_2}}=4$
2. B.$\frac{{\epsilon }_{r_1}}{{\epsilon }_{r_2}}=2$
3. C.$\frac{{\epsilon }_{r_1}}{{\epsilon }_{r_2}}=\frac{1}{4}$
4. D.$\frac{{\epsilon }_{r_1}}{{\epsilon }_{r_2}}=\frac{1}{2}$

The electric field component of a monochromatic radiation is given by $\vec{E}=2{\mathrm{E}}_0\hat{i}\cos kz\cos \omega t$ Its magnetic field $\vec{B}$ is then given by :

1. A.$\frac{2E_0}{c}\hat{j}\sin kz\cos \omega t$
2. B.$-\frac{2E_0}{c}\hat{j}\sin kz\sin \omega t$
3. C.$\frac{2E_0}{c}\hat{j}\sin kz\sin \omega t$
4. D.$\frac{2E_0}{c}\hat{j}\cos kz\cos \omega t$

1. A.${\Phi }_1<{\Phi }_2={\Phi }_3>{\Phi }_4$
2. B.${\Phi }_1>{\Phi }_2>{\Phi }_3>{\Phi }_4$
3. C.${\Phi }_1={\Phi }_2={\Phi }_3={\Phi }_4$
4. D.${\Phi }_1>{\Phi }_3;{\Phi }_2<{\Phi }_4$

1. A.$3$
2. B.$4$
3. C.$5$
4. D.$6$

There is a uniform electrostatic field in a region. The potential at various points on a small sphere centred at $P$, in the region, is found to vary between the limits 589.0 V to 589.8 V. What is the potential at a point on the sphere whose radius vector makes an angle of $60^{\circ }$ with the direction of the field ?

1. A.$589.5\mathrm{V}$
2. B.$589.2\mathrm{V}$
3. C.$589.4\mathrm{V}$
4. D.$589.6\mathrm{V}$

The energy stored in the electric field produced by a metal sphere is 4.5 J. If the sphere contains $4\mu \mathrm{C}$ charge, its radius will be : [ Take : $\frac{1}{4\pi {ϵ}_0}=9\times 10^9\mathrm{N}-{\mathrm{m}}^2/{\mathrm{C}}^2$ ]

1. A.$20\mathrm{mm}$
2. B.$32\mathrm{mm}$
3. C.$28\mathrm{mm}$
4. D.$16\mathrm{mm}$

In a certain region static electric and magnetic fields exist. The magnetic field is given by $\vec{B}=B_0\left(\hat{i}+2\hat{j}-4\hat{k}\right)$. If a test charge moving with a velocity $\vec{v}=v_0\left(3\hat{i}-\hat{j}+2\hat{k}\right)$ experiences no force in that region, then the electric field in the region, in SI units, is :

1. A.$\vec{E}=-v_0{B}_0\left(3\hat{i}-2\hat{j}-4\hat{k}\right)$
2. B.$\vec{E}=-v_0{B}_0\left(\hat{i}+\hat{j}+7\hat{k}\right)$
3. C.$\vec{E}=v_0{B}_0\left(14\hat{j}+7\hat{k}\right)$
4. D.$\vec{E}=-v_0{B}_0\left(14\hat{j}+7\hat{k}\right)$