Electrostatics & Capacitors · JEE Main previous year questions

1. A.$60\mu \text{C}$
2. B.$130\mu \text{C}$
3. C.$260\mu \text{C}$
4. D.$585\mu \text{C}$

1. A.$2\mu \text{F}$
2. B.$32\mu \text{F}$
3. C.$6\mu \text{F}$
4. D.$8\mu \text{F}$

Sixty four conducting drops each of radius 0.02 m and each carrying a charge of $5\mu \text{C}$ are combined to form a bigger drop. The ratio of surface charge density of bigger drop to the smaller drop will be :

1. A.1 : 4
2. B.4 : 1
3. C.1 : 8
4. D.8 : 1

1. A.$E_1=\sigma /{\epsilon }_0$, $E_2=\sigma /2{\epsilon }_0$
2. B.$E_1=2\sigma /{\epsilon }_0$, $E_2=\sigma /{\epsilon }_0$
3. C.$E_1=E_2=\sigma /2{\epsilon }_0$
4. D.$E_1=E_2=\sigma /{\epsilon }_0$

The electric field in an electromagnetic wave is given by $E=56.5\sin \omega (t-x/c){\text{ NC}}^{-1}$. Find the intensity of the wave if it is propagating along x-axis in the free space. (Given : ${\epsilon }_0=8.85\times 10^{-12}{\text{ C}}^2{\text{N}}^{-1}{\text{m}}^{-2}$)

1. A.$5.65{\text{ Wm}}^{-2}$
2. B.$4.24{\text{ Wm}}^{-2}$
3. C.$1.9\times 10^{-7}{\text{ Wm}}^{-2}$
4. D.$56.5{\text{ Wm}}^{-2}$

A light wave travelling linearly in a medium of dielectric constant $4$, is incident on the horizontal interface separating medium with air. The angle of incidence for which the total intensity of incident wave will be reflected back into the same medium will be : (Given : relative permeability of medium ${\mu }_r=1$)

1. A.$10^{\circ }$
2. B.$20^{\circ }$
3. C.$30^{\circ }$
4. D.$60^{\circ }$

Two metallic plates form a parallel plate capacitor. The distance between the plates is 'd'. A metal sheet of thickness $\frac{d}{2}$ and of area equal to area of each plate is introduced between the plates. What will be the ratio of the new capacitance to the original capacitance of the capacitor?

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

The electromagnetic waves travel in a medium at a speed of $2.0\times 10^{8}m/s$. The relative permeability of the medium is 1.0. The relative permittivity of the medium will be :

1. A.2.25
2. B.4.25
3. C.6.25
4. D.8.25

A light whose electric field vectors are completely removed by using a good polaroid, allowed to incident on the surface of the prism at Brewster's angle. Choose the most suitable option for the phenomenon related to the prism.

1. A.Reflected and refracted rays will be perpendicular to each other.
2. B.Wave will propagate along the surface of prism.
3. C.No refraction, and there will be total reflection of light.
4. D.No reflection, and there will be total transmission of light.

Two identical charged particles each having a mass $10\mathrm{g}$ and charge $2.0\times 10^{-7}\mathrm{C}$ are placed on a horizontal table with a separation of L between them such that they stay in limiting equilibrium. If the coefficient of friction between each particle and the table is 0.25, find the value of L. [Use $\mathrm{g}=10\mathrm{m}{\mathrm{s}}^{-2}$]

1. A.$12\mathrm{cm}$
2. B.$10\mathrm{cm}$
3. C.$8\mathrm{cm}$
4. D.$5\mathrm{cm}$

Given below are two statements : Statement I : The reactance of an ac circuit is zero. It is possible that the circuit contains a capacitor and an inductor. Statement II : In ac circuit, the average power delivered by the source never becomes zero. In the light of the above statements, choose the correct answer from the options given below.

1. A.Both Statement I and Statement II are true.
2. B.Both Statement I and Statement II are false.
3. C.Statement I is true but Statement II is false.
4. D.Statement I is false but Statement II is true.

If the charge on a capacitor is increased by 2 C, the energy stored in it increases by 44%. The original charge on the capacitor is (in C)

1. A.10
2. B.20
3. C.30
4. D.40

A monoatomic gas performs a work of $\frac{Q}{4}$ where Q is the heat supplied to it. The molar heat capacity of the gas will be ____ R during this transformation. Where R is the gas constant.

An antenna is placed in a dielectric medium of dielectric constant $6.25$. If the maximum size of that antenna is $5.0\mathrm{mm}$, it can radiate a signal of minimum frequency of ____ $\mathrm{GHz}$. (Given ${\mu }_r=1$ for dielectric medium)

1. A.$3.8\times 10^{-11}\text{ C}$
2. B.$8.3\times 10^{-11}\text{ C}$
3. C.$3.8\times 10^{-12}\text{ C}$
4. D.$8.3\times 10^{-12}\text{ C}$

A capacitor is connected to a $20\mathrm{V}$ battery through a resistance of $10\Omega$. It is found that the potential difference across the capacitor rises to $2\mathrm{V}$ in $1\mu \mathrm{s}$. The capacitance of the capacitor is ____ $\mu \mathrm{F}$. Given : $\ln \left(\frac{10}{9}\right)=0.105$

1. A.9.52
2. B.0.95
3. C.0.105
4. D.1.85

Electric field of plane electromagnetic wave propagating through a non-magnetic medium is given by $E=20\cos (2\times 10^{10}t-200x)V/m$. The dielectric constant of the medium is equal to : (Take ${\mu }_r=1$)

1. A.9
2. B.2
3. C.$\frac{1}{3}$
4. D.3

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 :

1. A.$\frac{Q}{2\pi {\epsilon }_0}\left[\frac{1}{a}+\frac{1}{\sqrt{s^2+a^2}}\right]$
2. B.$\frac{Q}{4\pi {\epsilon }_0}\left[\frac{1}{a}+\frac{1}{\sqrt{s^2+a^2}}\right]$
3. C.$\frac{Q}{4\pi {\epsilon }_0}\left[\frac{1}{a}-\frac{1}{\sqrt{s^2+a^2}}\right]$
4. D.$\frac{Q}{2\pi {\epsilon }_0}\left[\frac{1}{a}-\frac{1}{\sqrt{s^2+a^2}}\right]$

1. A.$\frac{{\epsilon }_{0}A}{d}\left(\frac{1}{2}+\frac{K_1{K}_2}{K_1+K_2}\right)$
2. B.$\frac{{\epsilon }_{0}A}{d}\left(\frac{1}{2}+\frac{K_1{K}_2}{2(K_1+K_2)}\right)$
3. C.$\frac{{\epsilon }_{0}A}{d}\left(\frac{1}{2}+\frac{K_1+K_2}{K_1{K}_2}\right)$
4. D.$\frac{{\epsilon }_{0}A}{d}\left(\frac{1}{2}+\frac{2(K_1+K_2)}{K_1{K}_2}\right)$

1. A.$5.9\text{ A}$
2. B.$3.16\text{ A}$
3. C.$0.94\text{ A}$
4. D.$6\text{ A}$

Match List I with List II. $$\begin{array}{llll}& \text{List - I}& & \text{List - II}\\ \text{(a)}& \text{Capacitance, C}& \text{(i)}& M^1{L}^1{T}^{-3}{A}^{-1}\\ \text{(b)}& \text{Permittivity of free space, }{\epsilon }_0& \text{(ii)}& M^{-1}{L}^{-3}{T}^4{A}^2\\ \text{(c)}& \text{Permeability of free space, }{\mu }_0& \text{(iii)}& M^{-1}{L}^{-2}{T}^4{A}^2\\ \text{(d)}& \text{Electric field, E}& \text{(iv)}& M^1{L}^1{T}^{-2}{A}^{-2}\end{array}$$ Choose the correct answer from the options given below

1. A.(a) $\to$ (iii), (b) $\to$ (ii), (c) $\to$ (iv), (d) $\to$ (i)
2. B.(a) $\to$ (iii), (b) $\to$ (iv), (c) $\to$ (ii), (d) $\to$ (i)
3. C.(a) $\to$ (iv), (b) $\to$ (ii), (c) $\to$ (iii), (d) $\to$ (i)
4. D.(a) $\to$ (iv), (b) $\to$ (iii), (c) $\to$ (ii), (d) $\to$ (i)

1. A.${\tan }^{-1}\left[\frac{q}{mg}\times \frac{C_1(V_2-V_1)}{(C_1+C_2)(d-t)}\right]$
2. B.${\tan }^{-1}\left[\frac{q}{mg}\times \frac{C_2(V_2-V_1)}{(C_1+C_2)(d-t)}\right]$
3. C.${\tan }^{-1}\left[\frac{q}{mg}\times \frac{C_2(V_1+V_2)}{(C_1+C_2)(d-t)}\right]$
4. D.${\tan }^{-1}\left[\frac{q}{mg}\times \frac{C_1(V_1+V_2)}{(C_1+C_2)(d-t)}\right]$

1. A.$\frac{1}{4\pi {\epsilon }_0}\frac{q}{l^2}$
2. B.$\frac{1}{4\pi {\epsilon }_0}\frac{q}{(2l^2)}\left(2\sqrt{2}-1\right)$
3. C.$\frac{q}{4\pi {\epsilon }_0(2l{)}^2}$
4. D.$\frac{1}{4\pi {\epsilon }_0}\frac{2q}{2l^2}\left(\sqrt{2}\right)$

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 $\left(0<x\le \frac{d}{2}\right)$ $\epsilon (x)={\epsilon }_0+k(d-x)$, for $\left(\frac{d}{2}\le x\le d\right)$

1. A.${\left({\epsilon }_0+\frac{kd}{2}\right)}^{2/kA}$
2. B.$\frac{kA}{2\ln \left(\frac{2{\epsilon }_0+kd}{2{\epsilon }_0}\right)}$
3. C.0
4. D.$\frac{kA}{2}\ln \left(\frac{2{\epsilon }_0}{2{\epsilon }_0-kd}\right)$