Electrostatics & Capacitors · JEE Main previous year questions

Suppose a uniformly charged wall provides a uniform electric field of $2\times 10^4\text{ N/C}$ normally. A charged particle of mass $2\text{ g}$ being suspended through a silk thread of length $20\text{ cm}$ and remain stayed at a distance of $10\text{ cm}$ from the wall. Then the charge on the particle will be $\frac{1}{\sqrt{x}}\mu \text{C}$ where $x=$ ________ . $[\text{use }g=10{\text{ m/s}}^2]$

Two charges $q$ and $3q$ are separated by a distance '$r$' in air. At a distance $x$ from charge $q$, the resultant electric field is zero. The value of $x$ is :

1. A.$\frac{r}{3(1+\sqrt{3})}$
2. B.$\frac{(1+\sqrt{3})}{r}$
3. C.$\frac{r}{(1+\sqrt{3})}$
4. D.$r(1+\sqrt{3})$

In a plane EM wave, the electric field oscillates sinusoidally at a frequency of $5\times 10^{10}\mathrm{Hz}$ and an amplitude of $50\mathrm{V}{\mathrm{m}}^{-1}$. The total average energy density of the electromagnetic field of the wave is : [Use ${\epsilon }_0=8.85\times 10^{-12}{\mathrm{C}}^2/N{\mathrm{m}}^2$ ]

1. A.$4.425\times 10^{-8}\mathrm{J}{\mathrm{m}}^{-3}$
2. B.$2.212\times 10^{-10}\mathrm{J}{\mathrm{m}}^{-3}$
3. C.$2.212\times 10^{-8}\mathrm{J}{\mathrm{m}}^{-3}$
4. D.$1.106\times 10^{-8}\mathrm{J}{\mathrm{m}}^{-3}$

A parallel plate capacitor with plate separation $5\mathrm{mm}$ is charged up by a battery. It is found that on introducing a dielectric sheet of thickness $2\mathrm{mm}$, while keeping the battery connections intact, the capacitor draws $25\%$ more charge from the battery than before. The dielectric constant of the sheet is ____.

Force between two point charges $q_1$ and $q_2$ placed in vacuum at '$r$' cm apart is $F$. Force between them when placed in a medium having dielectric constant $K=5$ at '$r/5$' cm apart will be:

1. A.$5F$
2. B.$25F$
3. C.$F/5$
4. D.$F/25$

The electrostatic potential due to an electric dipole at a distance '$r$' varies as :

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

The electric field of an electromagnetic wave in free space is represented as $\vec{E}=E_0\cos (\omega t-kz)\hat{i}$. The corresponding magnetic induction vector will be :

1. A.$\vec{B}=E_{0}C\cos (\omega t+kz)\hat{j}$
2. B.$\vec{B}=\frac{E_0}{C}\cos (\omega t-kz)\hat{j}$
3. C.$\vec{B}=E_{0}C\cos (\omega t-kz)\hat{j}$
4. D.$\vec{B}=\frac{E_0}{C}\cos (\omega t+kz)\hat{j}$

A capacitor of capacitance $C$ and potential $\mathrm{V}$ has energy $\mathrm{E}$. It is connected to another capacitor of capacitance $2C$ and potential $2\text{ V}$. Then the loss of energy is $\frac{x}{3}\mathrm{E}$, where $x$ is _________.

A capacitor of capacitance $100\mu \text{F}$ is charged to a potential of $12\text{ V}$ and connected to a $6.4\text{ mH}$ inductor to produce oscillations. The maximum current in the circuit would be :

1. A.$2.0\text{ A}$
2. B.$3.2\text{ A}$
3. C.$1.5\text{ A}$
4. D.$1.2\text{ A}$

Two charges of $5Q$ and $-2Q$ are situated at the points $(3a,0)$ and $(-5a,0)$ respectively. The electric flux through a sphere of radius '$4a$' having center at origin is :

1. A.$\frac{2Q}{{\epsilon }_0}$
2. B.$\frac{7Q}{{\epsilon }_0}$
3. C.$\frac{3Q}{{\epsilon }_0}$
4. D.$\frac{5Q}{{\epsilon }_0}$

Match List I with List II | | List - I | | List - II | | :--- | :--- | :--- | :--- | | (A) | $\oint \vec{B}\cdot \overrightarrow{dl}={\mu }_o{i}_c+{\mu }_o{\epsilon }_o\frac{d{\varphi }_E}{dt}$ | (I) | Gauss' law for electricity | | (B) | $\oint \vec{E}\cdot \overrightarrow{dl}=\frac{d{\varphi }_B}{dt}$ | (II) | Gauss' law for magnetism | | (C) | $\oint \vec{E}\cdot \overrightarrow{dA}=\frac{Q}{{\epsilon }_o}$ | (III) | Faraday law | | (D) | $\oint \vec{B}\cdot \overrightarrow{dA}=0$ | (IV) | Ampere - Maxwell law | Choose the correct answer from the options given below:

1. A.A-IV, B-III, C-I, D-II
2. B.A-I, B-II, C-III, D-IV
3. C.A-IV, B-I, C-III, D-II
4. D.A-II, B-III, C-I, D-IV

The electric current through a wire varies with time as $I=I_0+\beta t$, where $I_0=20\text{ A}$ and $\beta =3\text{ A/s}$. The amount of electric charge crossed through a section of the wire in $20\text{ s}$ is :

1. A.$80\text{ C}$
2. B.$800\text{ C}$
3. C.$1000\text{ C}$
4. D.$1600\text{ C}$

An electron is moving under the influence of the electric field of a uniformly charged infinite plane sheet S having surface charge density $+\sigma$. The electron at $t=0$ is at a distance of $1\text{ m}$ from $S$ and has a speed of $1\text{ m/s}$. The maximum value of $\sigma$ if the electron strikes $S$ at $t=1\text{ s}$ is $\alpha \left[\frac{m{\epsilon }_0}{e}\right]\frac{\text{C}}{{\text{m}}^2}$, the value of $\alpha$ is _______.

An electric field is given by $(6\hat{i}+5\hat{j}+3\hat{k})\text{N/C}$. The electric flux through a surface area $30\hat{i}{\text{ m}}^2$ lying in YZ-plane (in SI unit) is :

1. A.60
2. B.90
3. C.180
4. D.150

An electric charge $10^{-6}\mu \text{C}$ is placed at origin $(0,0)\text{ m}$ of $X-Y$ co-ordinate system. Two points P and Q are situated at $(\sqrt{3},\sqrt{3})\text{m}$ and $(\sqrt{6},0)\text{m}$ respectively. The potential difference between the points P and Q will be :

1. A.$\sqrt{3}\text{ V}$
2. B.$\sqrt{6}\text{ V}$
3. C.$0\text{ V}$
4. D.$3\text{ V}$

A thin metallic wire having cross sectional area of $10^{-4}{\text{ m}}^2$ is used to make a ring of radius $30\text{ cm}$. A positive charge of $2\pi \text{ C}$ is uniformly distributed over the ring, while another positive charge of $30\text{ pC}$ is kept at the centre of the ring. The tension in the ring is _____ $\text{N}$; provided that the ring does not get deformed (neglect the influence of gravity). (given, $\frac{1}{4\pi {ϵ}_0}=9\times 10^9\text{ SI units}$)

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Work done by electric field on moving a positive charge on an equipotential surface is always zero. Reason (R) : Electric lines of forces are always perpendicular to equipotential surfaces. In the light of the above statements, choose the most appropriate answer from the options given below :

1. A.Both (A) and (R) are correct and (R) is the correct explanation of (A)
2. B.(A) is correct but (R) is not correct
3. C.Both (A) and (R) are correct but (R) is not the correct explanation of (A)
4. D.(A) is not correct but (R) is correct

Two charges of $-4\mu \text{C}$ and $+4\mu \text{C}$ are placed at the points $\text{A}(1,0,4)\text{m}$ and $\text{B}(2,-1,5)\text{m}$ located in an electric field $\vec{\text{E}}=0.20\hat{i}\text{ V/cm}$. The magnitude of the torque acting on the dipole is $8\sqrt{\alpha }\times 10^{-5}\text{Nm}$, where $\alpha =$ _______.

The source of time varying magnetic field may be (A) a permanent magnet (B) an electric field changing linearly with time (C) direct current (D) a decelerating charge particle (E) an antenna fed with a digital signal Choose the correct answer from the options given below:

1. A.(D) only
2. B.(A) only
3. C.(B) and (D) only
4. D.(C) and (E) only

Two charges each of magnitude $0.01\text{ C}$ and separated by a distance of $0.4\text{ mm}$ constitute an electric dipole. If the dipole is placed in an uniform electric field '$\vec{E}$' of $10\text{ dyne/C}$ making $30^{\circ }$ angle with $\vec{E}$, the magnitude of torque acting on dipole is:

1. A.$4.0\times 10^{-10}\text{ Nm}$
2. B.$1.5\times 10^{-9}\text{ Nm}$
3. C.$1.0\times 10^{-8}\text{ Nm}$
4. D.$2.0\times 10^{-10}\text{ Nm}$

A thin infinite sheet charge and an infinite line charge of respective charge densities $+\sigma$ and $+\lambda$ are placed parallel at $5\text{ m}$ distance from each other. Points 'P' and 'Q' are at $\frac{3}{\pi }\text{ m}$ and $\frac{4}{\pi }\text{ m}$ perpendicular distances from line charge towards sheet charge, respectively. '${\mathrm{E}}_P$' and '${\mathrm{E}}_Q$' are the magnitudes of resultant electric field intensities at point 'P' and 'Q', respectively. If $\frac{{\mathrm{E}}_P}{{\mathrm{E}}_Q}=\frac{4}{a}$ for $2|\sigma |=|\lambda |$, then the value of $a$ is ___________.

In an electromagnetic wave, at an instant and at particular position, the electric field is along the negative $z$-axis and magnetic field is along the positive $x$-axis. Then the direction of propagation of electromagnetic wave is:

1. A.at $45^{\circ }$ angle from positive y-axis
2. B.positive $y$-axis
3. C.negative $y$-axis
4. D.positive z-axis