Electrostatics & Capacitors · JEE Main previous year questions

Magnetic field in a plane electromagnetic wave is given by $\vec{B}={\mathrm{B}}_0\sin (k\mathrm{x}+\omega t)\hat{j}T$ Expression for corresponding electric field will be : Where c is speed of light.

1. A.$\vec{E}={\mathrm{B}}_0\mathrm{c}\sin (k\mathrm{x}+\omega t)\hat{k}V/m$
2. B.$\vec{E}=\frac{B_0}{c}\sin (k\mathrm{x}+\omega t)\hat{k}V/m$
3. C.$\vec{E}=-{\mathrm{B}}_0\mathrm{c}\sin (\mathrm{kx}+\omega t)\hat{k}V/m$
4. D.$\vec{E}={\mathrm{B}}_0\mathrm{c}\sin (\mathrm{kx}-\omega t)\hat{k}V/m$

1. A.$420N/C$
2. B.$480N/C$
3. C.$240N/C$
4. D.$360N/C$

1. A.$\frac{2Q}{\pi (a^2-b^2)}$
2. B.$\frac{2Q}{\pi a^2}$
3. C.$\frac{Q}{2\pi a^2}$
4. D.$\frac{Q}{2\pi (b^2-a^2)}$

A solid body of constant heat capacity $1\mathrm{J}{/}^{\circ }\mathrm{C}$ is being heated by keeping it in contact with reservoirs in two ways: $(i)$ Sequentially keeping in contact with 2 reservoirs such that each reservoir supplies same amount of heat. $(ii)$ Sequentially keeping in contact with 8 reservoirs such that each reservoir supplies same amount of heat. In both the cases body is brought from initial temperature $100^{\circ }\mathrm{C}$ to final temperature $200^{\circ }\mathrm{C}$. Entropy change of the body in the two cases respectively is :

1. A.$\ln 2,2\ln 2$
2. B.$2\ln 2,8\ln 2$
3. C.$\ln 2,4\ln 2$
4. D.$\ln 2,\ln 2$

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

A uniformly charged solid sphere of radius $R$ has potential $V_0$ (measured with respect to $\infty$) on its surface. For this sphere the equipotential surfaces with potentials $\frac{3V_0}{2}$, $\frac{5V_0}{4}$, $\frac{3V_0}{4}$ and $\frac{V_0}{4}$ have radius $R_1$, $R_2$, $R_3$ and $R_4$ respectively. Then

1. A.$R_1=0\text{ and }{R}_2<(R_4-R_3)$
2. B.$2R<R_4$
3. C.$R_1=0\text{ and }{R}_2>(R_4-R_3)$
4. D.$R_1\ne 0\text{ and }(R_2-R_1)>(R_4-R_3)$

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

Assume that an electric field $\vec{E}=30x^2\hat{i}$ exists in space. Then the potential difference $V_A-V_O$, where $V_O$ is the potential at the origin and $V_A$ the potential at $x=2\mathrm{m}$ is :

1. A.$120J/C$
2. B.$-120J/C$
3. C.$-80J/C$
4. D.$80J/C$

A parallel plate capacitor is made of two circular plates separated by a distance $5\mathrm{mm}$ and with a dielectric of dielectric constant $2.2$ between them. When the electric field in the dielectric is $3\times 10^{4}V/m$ the charge density of the positive plate will be close to:

1. A.$6\times 10^{-7}C/{\mathrm{m}}^2$
2. B.$3\times 10^{-7}C/{\mathrm{m}}^2$
3. C.$3\times 10^{4}C/{\mathrm{m}}^2$
4. D.$6\times 10^{4}C/{\mathrm{m}}^2$

In a large building, there are 15 bulbs of $40\mathrm{W}$, 5 bulbs of $100\mathrm{W}$, 5 fans of $80\mathrm{W}$ and 1 heater of $1\mathrm{kW}$. The voltage of electric mains is $220\mathrm{V}$. The minimum capacity of the main fuse of the building will be:

1. A.$8\mathrm{A}$
2. B.$10\mathrm{A}$
3. C.$12\mathrm{A}$
4. D.$14\mathrm{A}$

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

This question has Statement 1 and Statement 2. Of the four choices given after the Statements, choose the one that best describes the two Statements. Statement 1: It is not possible to make a sphere of capacity 1 farad using a conducting material. Statement 2: It is possible for earth as its radius is $6.4\times 10^6\mathrm{m}$.

1. A.Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation of Statement 1.
2. B.Statement 1 is false, Statement 2 is true.
3. C.Statement 1 is true, Statement 2 is true, Statement 2 is not the correct explanation of Statement 1.
4. D.Statement 1 is true, Statement 2 is false.

The capacitor of an oscillatory circuit is enclosed in a container. When the container is evacuated, the resonance frequency of the circuit is $10\mathrm{kHz}$. When the container is filled with a gas, the resonance frequency changes by $50\mathrm{Hz}$. The dielectric constant of the gas is

1. A.$1.001$
2. B.$2.001$
3. C.$1.01$
4. D.$3.01$

A radio transmitter transmits at $830\mathrm{kHz}$. At a certain distance from the transmitter magnetic field has amplitude $4.82\times 10^{-11}\mathrm{T}$. The electric field and the wavelength are respectively

1. A.$0.014N/C,36\mathrm{m}$
2. B.$0.14N/C,36\mathrm{m}$
3. C.$0.14N/C,360\mathrm{m}$
4. D.$0.014N/C,360\mathrm{m}$

A series combination of $n_1$ capacitors, each of capacity $C_1$ is charged by source of potential difference $4V$. When another parallel combination of $n_2$ capacitors each of capacity $C_2$ is charged by a source of potential difference $V$, it has the same total energy stored in it as the first combination has. The value of $C_2$ in terms of $C_1$ is then

1. A.$16\frac{n_2}{n_1}{C}_1$
2. B.$\frac{2C_1}{n_1{n}_2}$
3. C.$2\frac{n_2}{n_1}{C}_1$
4. D.$\frac{16C_1}{n_1{n}_2}$

The electric potential $V(x)$ in a region around the origin is given by $V(x)=4x^2$ volts. The electric charge enclosed in a cube of $1\mathrm{m}$ side with its centre at the origin is (in coulomb)

1. A.$8{\epsilon }_0$
2. B.$-4{\epsilon }_0$
3. C.0
4. D.$-8{\epsilon }_0$

1. A.No charge flows in (a) but charge flows from $R$ to $L$ in (b)
2. B.Charges flow from $L$ to $R$ in both (a) and (b)
3. C.Charges flow from $R$ to $L$ in (a) and from $L$ to $R$ in (b)
4. D.No charge flows in (a) but charge flows from $L$ to $R$ in (b)

The velocity of certain ions that pass undeflected through crossed electric field $E=7.7kV/m$ and magnetic field $B=0.14\mathrm{T}$ is

1. A.$18km/s$
2. B.$77km/s$
3. C.$55km/s$
4. D.$1078km/s$

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of $30^{\circ }$ with each other. When suspended in a liquid of density $0.8\mathrm{g}\mathrm{c}{\mathrm{m}}^{-3}$, the angle remains the same. If density of the material of the sphere is $1.6\mathrm{g}\mathrm{c}{\mathrm{m}}^{-3}$, the dielectric constant of the liquid is

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

1. A.$\frac{q}{4{\pi }^2{\epsilon }_0{r}^2}\hat{j}$
2. B.$-\frac{q}{4{\pi }^2{\epsilon }_0{r}^2}\hat{j}$
3. C.$-\frac{q}{2{\pi }^2{\epsilon }_0{r}^2}\hat{j}$
4. D.$\frac{q}{2{\pi }^2{\epsilon }_0{r}^2}\hat{j}$

Let there be a spherically symmetric charge distribution with charge density varying as $\rho (r)={\rho }_0\left(\frac{5}{4}-\frac{r}{R}\right)$ upto $r=R$, and $\rho (r)=0$ for $r>R$, where $r$ is the distance from the origin. The electric field at a distance $r$ ($r<R$) from the origin is given by

1. A.$\frac{{\rho }_{0}r}{4{\epsilon }_0}\left(\frac{5}{3}-\frac{r}{R}\right)$
2. B.$\frac{4\pi {\rho }_{0}r}{3{\epsilon }_0}\left(\frac{5}{3}-\frac{r}{R}\right)$
3. C.$\frac{4{\rho }_{0}r}{4{\epsilon }_0}\left(\frac{5}{4}-\frac{r}{R}\right)$
4. D.$\frac{{\rho }_{0}r}{3{\epsilon }_0}\left(\frac{5}{4}-\frac{r}{R}\right)$

Let $C$ be the capacitance of a capacitor discharging through a resistor $R$. Suppose $t_1$ is the time taken for the energy stored in the capacitor to reduce to half its initial value and $t_2$ is the time taken for the charge to reduce to one-fourth its initial value. Then the ratio $t_1/t_2$ will be

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

In a series $LCR$ circuit $R=200\Omega$ and the voltage and the frequency of the main supply are $220\mathrm{V}$ and $50\mathrm{Hz}$ respectively. On taking out the capacitance from the circuit the current lags behind the voltage by $30^{\circ }$. On taking out the inductor from the circuit the current leads the voltage by $30^{\circ }$. The power dissipated in the $LCR$ circuit is

1. A.$305\mathrm{W}$
2. B.$210\mathrm{W}$
3. C.zero
4. D.$242\mathrm{W}$

A charge $Q$ is placed at each of the opposite corners of a square. A charge $q$ is placed at each of the other two corners. If the net electrical force on $Q$ is zero, then $Q/q$ equals:

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

(This question contains Statement-1 and Statement-2. Of the four choices given after the statements, choose the one that best describes the two statements.) Statement-1 : For a charged particle moving from point $P$ to point $Q$, the net work done by an electrostatic field on the particle is independent of the path connecting point $P$ to point $Q$. Statement-2 : The net work done by a conservative force on an object moving along a closed loop is zero.

1. A.Statement-1 is true, Statement-2 is true; Statement-2 is the correct explanation of Statement-1.
2. B.Statement-1 is true, Statement-2 is true; Statement-2 is not the correct explanation of Statement-1.
3. C.Statement- 1 is false, Statement- 2 is true.
4. D.Statement- 1 true, Statement- 2 is false