Electrostatics Practice Questions

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R. Assertion A: Work done in moving a test charge between two points inside a uniformly charged spherical shell is zero, no matter which path is chosen. Reason R : Electrostatic potential inside a uniformly charged spherical shell is constant and is same as that on the surface of the shell. In the light of the above statements, choose the correct answer from the options given below

The electric flux is $\varphi =\alpha \sigma +\beta \lambda$Where $\lambda$ and $\sigma$ are linear and surface charge density, respectively. $(\;\frac{\alpha }{\beta })$ represents

In the first configuration (1 ) as shown in the figure, four identical charges $(q_0)$ are kept at the corners $A$, $B, C$ and $D$ of square of side length ' $a$ '. In the second configuration (2 ), the same charges are shifted to mid points $G, E, H$ and $F$, of the square. If $K=\;\frac{1}{4 \pi \epsilon _0}$, the difference between the potential energies of configuration (2 ) and (1 ) is given by

An electric dipole of mass $m$, charge $q$, and length $I$ is placed in a uniform electric field $\vec{E}=E_0 \hat{i}$. When the dipole is rotated slightly from its equilibrium position and released, the time period of its oscillations will be :

Two charges $q_1$ and $q_2$ are separated by a distance of 30 cm . A third charge $q_3$ initially at ' $C$ ' as shown in the figure, is moved along the circular path of radius 40 cm from C to D . If the difference in potential energy due to movement of $q_3$ from C to D is given by $\;\frac{q_3 K}{4 \pi \epsilon _0}$ the value of $K$ is

A square loop of side $a=1 {\text{m}}$ is held normally in front of a point charge $q=1 {\text{C}}$. The flux of the electric field through the shaded region is $\;\frac{5}{p} \times \;\frac{1}{\epsilon _0} \;{ {\text{Nm}}^2}/{ {\text{C}}}$, where the value of $p$ is _____

A point charge $+q$ is placed at the origin. A second point charge $+9 q$ is placed at $(d, 0,0)$ in Cartesian coordinate system. The point in between them where the electric field vanishes is:

Two metal spheres of radius $R$ and $3 R$ have same surface charge density $\sigma$. If they are brought in contact and then separated, the surface charge density on smaller and bigger sphere becomes $\sigma _1$ and $\sigma _2$, respectively. The ratio $\;\frac{\sigma _1}{\sigma _2}$ is

A small uncharged conducting sphere is placed in contact with an identical sphere but having $4 \times 10^{-8} {\text{C}}$ charge and then removed to a distance such that the force of repulsion between them is $9 \times 10^{-3} {\text{N}}$. The distance between them is (Take $\;\frac{1}{4 \pi \epsilon _0}$ as $9 \times 10^9$ in SI units)

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Net dipole moment of a polar linear isotropic dielectric substance is not zero even in the absence of an external electric field. Reason (R) : In absence of an external electric field, the different permanent dipoles of a polar dielectric substance are oriented in random directions. In the light of the above statements, choose the most appropriate answer from the options given below.

Two point charges $-4 \mu {\text{C}}$ and $4 \mu {\text{C}}$, constituting an electric dipole, are placed at $(-9,0,0) {\text{cm}}$ and $(9,0,0) {\text{cm}}$ in a uniform electric field of strength $10^4 {\text{NC}}^{-1}$. The work done on the dipole in rotating it from the equilibrium through $180^{\circ}$ is

Two large plane parallel conducting plates are kept 10 cm apart as shown in figure. The potential difference between them is $V$. The potential difference between the points $A$ and $B$ (shown in the figure) is

The electrostatic potential on the surface of uniformly charged spherical shell of radius $R=10 {\text{cm}}$ is 120 V . The potential at the centre of shell, at a distance $r=5$ cm from centre, and at a distance $r=15 {\text{cm}}$ from the centre of the shell respectively, are:

An infinitely long wire has uniform linear charge density $\lambda =2 {\text{nC}} / {\text{m}}$. The net flux through a Gaussian cube of side length ${\sqrt{3}} {\text{cm}}$, if the wire passes through any two corners of the cube, that are maximally displaced from each other, would be $x {\text{Nm}}^2 {\text{C}}^{-1}$, where $x$ is$[Neglect any edge effects and use $\;\frac{1}{4 π ε_0}=9 × 10^9$ SI units]$

A small bob of mass 100 mg and charge $+10 \mu {\text{C}}$ is connected to an insulating string of length 1 m . It is brought near to an infinitely long non-conducting sheet of charge density ' $\sigma$ ' as shown in figure. If string subtends and angle of $45^{\circ}$ with the sheet at equilibrium the charge density of sheet will be. $\{.$ Given $\epsilon _0=8.85 \times 10^{-12} \;{ {\text{F}}}/{ {\text{m}}}$ and acceleration due to gravity, $g=10 \;{ {\text{m}}}/{ {\ s}^2}\}$

Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : The outer body of an air craft is made of metal which protects persons sitting inside from lightning-strikes. Reason (R) : The electric field inside the cavity enclosed by a conductor is zero. In the light of the above statements, choose the most appropriate answer from the options given below:

An electric dipole of dipole moment $6 \times 10^{-6} {\text{Cm}}$ is placed in uniform electric field of magnitude $10^6$ ${\text{V}} / {\text{m}}$. Initially, the dipole moment is parallel to electric field. The work that needs to be done on the dipole to make its dipole moment opposite to the field, will be ______ J.

A particle of mass ' $m$ ' and charge ' $q$ ' is fastened to one end ' $A$ ' of a massless string having equilibrium length $I$, whose other end is fixed at point ' $O$ '. The whole system is placed on a frictionless horizontal plane and is initially at rest. If uniform electric field is switched on along the direction as shown in figure, then the speed of the particle when it crosses the $x$-axis is