Electrostatics & Capacitors · JEE Main previous year questions

Let $P(r)=\frac{Q}{\pi R^4}r$ be the charge density distribution for a solid sphere of radius $R$ and total charge $Q$. For a point '$p$' inside the sphere at distance $r_1$ from the center of the sphere, the magnitude of electric field is :

1. A.$\frac{Q}{4\pi {ϵ}_0{r}_1^2}$
2. B.$\frac{Q{r}_1^2}{4\pi {ϵ}_0{R}^4}$
3. C.$\frac{Q{r}_1^2}{3\pi {ϵ}_0{R}^4}$
4. D.0

Two rigid boxes containing different ideal gases are placed on a table. Box A contains one mole of nitrogen at temperature $T_0$, while Box contains one mole of helium at temperature $(\frac{7}{3})T_0$. The boxes are then put into thermal contact with each other, and heat flows between them until the gases reach a common final temperature (ignore the heat capacity of boxes). Then, the final temperature of the gases, $T_f$ in terms of $T_0$ is

1. A.$T_f=\frac{3}{7}{T}_0$
2. B.$T_f=\frac{7}{3}{T}_0$
3. C.$T_f=\frac{3}{2}{T}_0$
4. D.$T_f=\frac{5}{2}{T}_0$

An electric dipole is placed at an angle of $30^{\circ }$ to a non-uniform electric field. The dipole will experience

1. A.a translation force only in the direction of the field
2. B.a translation force only in a direction normal to the direction of the field
3. C.a torque as well as a translational force
4. D.a torque only

Two spherical conductors $A$ and $B$ of radii $1mm$ and $2mm$ are separated by a distance of $5cm$ and are uniformly charged. If the spheres are connected by a conducting wire then in equilibrium condition, the ratio of the magnitude of the electric fields at the surfaces of spheres $A$ and $B$ is

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

The $rms$ value of the electric field of the light coming from the Sun is $720N/C$. The average total energy density of the electromagnetic wave is

1. A.$4.58\times 10^{-6}J/{\mathrm{m}}^3$
2. B.$6.37\times 10^{-9}J/{\mathrm{m}}^3$
3. C.$81.35\times 10^{-12}J/{\mathrm{m}}^3$
4. D.$3.3\times 10^{-3}J/{\mathrm{m}}^3$

Two point charges $+8q$ and $-2q$ are located at $x=0$ and $x=L$ respectively. The location of a point on the $x$ axis at which the net electric field due to these two point charges is zero is

1. A.$\frac{L}{4}$
2. B.$2L$
3. C.$4L$
4. D.$8L$

Two thin wire rings each having a radius $R$ are placed at a distance $d$ apart with their axes coinciding. The charges on the two rings are $+q$ and $-q$. The potential difference between the centres of the two rings is

1. A.$\frac{q}{2\pi {ϵ}_0}\left[\frac{1}{R}-\frac{1}{\sqrt{R^2+d^2}}\right]$
2. B.$\frac{qR}{4\pi {ϵ}_0{d}^2}$
3. C.$\frac{q}{4\pi {ϵ}_0}\left[\frac{1}{R}-\frac{1}{\sqrt{R^2+d^2}}\right]$
4. D.$\mathrm{zero}$

A parallel plate capacitor is made by stacking $n$ equally spaced plates connected alternatively. If the capacitance between any two adjacent plates is '$C$' then the resultant capacitance is

1. A.$(n+1)C$
2. B.$(n-1)C$
3. C.$nC$
4. D.$C$

1. A.$\cot \theta$
2. B.$\cos \theta$
3. C.$\tan \theta$
4. D.$\sin \theta$

A fully charged capacitor has a capacitance '$C$'. It is discharged through a small coil of resistance wire embedded in a thermally insulated block of specific heat capacity '$s$' and mass '$m$'. If the temperature of the block is raised by '$\Delta T$', the potential difference '$v$' across the capacitor is

1. A.$\frac{mC\Delta T}{s}$
2. B.$\sqrt{\frac{2mC\Delta T}{s}}$
3. C.$\sqrt{\frac{2ms\Delta T}{C}}$
4. D.$\frac{ms\Delta T}{C}$

Two voltmeters, one of copper and another of silver, are joined in parallel. When a total charge $q$ flows through the voltmeters, equal amount of metals are deposited. If the electrochemical equivalents of copper and silver are $Z_1$ and $Z_2$ respectively the charge which flows through the silver voltmeter is

1. A.$\frac{q}{1+\frac{Z_2}{Z_1}}$
2. B.$\frac{q}{1+\frac{Z_1}{Z_2}}$
3. C.$q\frac{Z_2}{Z_1}$
4. D.$q\frac{Z_1}{Z_2}$

A uniform electric field and a uniform magnetic field are acting along the same direction in a certain region. If an electron is projected along the direction of the fields with a certain velocity then

1. A.its velocity will increase
2. B.Its velocity will decrease
3. C.it will turn towards left of a direction of motion
4. D.it will turn towards right of direction of motion

The self inductance of the motor of an electric fan is $10\mathrm{H}$. In order to impart maximum power at $50\mathrm{Hz}$, it should be connected to a capacitance of

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

Two spherical conductors $B$ and $C$ having equal radii and carrying equal charges on them repel each other with a force $F$ when kept apart at some distance. A third spherical conductor having same radius as that of $B$ but uncharged is brought in contact with $B$, then brought in contact with $C$ and finally removed away from both. The new force of repulsion between $B$ and $C$ is

1. A.$F/8$
2. B.$3F/4$
3. C.$F/4$
4. D.$3F/8$

A charged particle ${}^{\prime }{q}^{\prime }$ is shot towards another charged particle ${}^{\prime }{Q}^{\prime }$ which is fixed, with a speed ${}^{\prime }{v}^{\prime }$. It approaches ${}^{\prime }{Q}^{\prime }$ upto a closest distance $r$ and then returns. If $q$ were given a speed of ${}^{\prime }2v^{\prime }$ the closest distance of approach would be

1. A.$r/2$
2. B.$2r$
3. C.$r$
4. D.$r/4$

Four charges equal to -$Q$ are placed at the four corners of a square and a charge $q$ is at its center. If the system is in equilibrium the value of $q$ is

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

A charged oil drop is suspended in a uniform field of $3\times 10^{4}v/m$ so that it neither falls nor rises. The charge on the drop will be (Take the mass of the charge $=9.9\times 10^{-15}\mathrm{kg}$ and $g=10m/{\mathrm{s}}^2$)

1. A.$1.6\times 10^{-18}\mathrm{C}$
2. B.$3.2\times 10^{-18}\mathrm{C}$
3. C.$3.3\times 10^{-18}\mathrm{C}$
4. D.$4.8\times 10^{-18}\mathrm{C}$

The electrochemical equivalent of a metal is $3.3\times 10^{-7}\mathrm{kg}$ per Coulomb. The mass of the metal liberated at the cathode when a $3\mathrm{A}$ current is passed for $2$ seconds will be

1. A.$6.6\times 10^{-7}\mathrm{kg}$
2. B.$9.9\times 10^{-7}\mathrm{kg}$
3. C.$19.8\times 10^{-7}\mathrm{kg}$
4. D.$1.1\times 10^{-7}\mathrm{kg}$

An electromagnetic wave of frequency $v=3.0\mathrm{MHz}$ passes from vacuum into a dielectric medium with permittivity $ϵ=4.0$. Then

1. A.wave length is halved and frequency remains unchanged
2. B.wave length is doubled and the frequency becomes half
3. C.wave length is doubled and the frequency remains unchanged
4. D.wave length and frequency both remain unchanged.

On moving a charge of $20$ coulomb by $2\mathrm{cm}$, $2\mathrm{J}$ of work is done, then the potential difference between the points is

1. A.$0.1\mathrm{V}$
2. B.$8\mathrm{V}$
3. C.$2\mathrm{V}$
4. D.$0.5\mathrm{V}$.

If there are $n$ capacitors in parallel connected to $V$ volt source, then the energy stored is equal to

1. A.$CV$
2. B.$\frac{1}{2}nC{V}^2$
3. C.$C{V}^2$
4. D.$\frac{1}{2n}C{V}^2$

1. A.$q/4\pi {ϵ}_{0}L$
2. B.zero
3. C.$q/2\pi {ϵ}_{0}L$
4. D.$q/3\pi {ϵ}_{0}L$

If a charge $q$ is placed at the center of the line joining two equal charges $Q$ such that the system is in equilibrium then the value of $q$ is

1. A.$Q/2$
2. B.$-Q/2$
3. C.$Q/4$
4. D.$-Q/4$

Capacitance (in $\mathrm{F}$) of a spherical conductor with radius $1\mathrm{m}$ is

1. A.$1.1\times 10^{-10}$
2. B.$10^{-6}$
3. C.$9\times 10^{-9}$
4. D.$10^{-3}$