Electrostatics Practice Questions

A positive ion $A$ and a negative ion $B$ has charges $6.67 \times 10^{-19} {\text{C}}$ and $9.6 \times 10^{-10} {\text{C}}$, and masses 19.2 $\times 10^{-27} {\text{kg}}$ and $9 \times 10^{-27} {\text{kg}}$ respectively. At an instant, the ions are separated by a certain distance $r$. At that instant the ratio of the magnitudes of electrostatic force to gravitational force is $P \times 10^{-23}$, where the value of $P$ is ______ (Take $\;\frac{1}{4 \pi \epsilon _0}=9 \times 10^9 {\text{Nm}}^2 {\text{C}}^{-1}$ and universal gravitational constant as $6.67 \times 10^{-11} {\text{Nm}}^2 {\text{kg}}^{-2}$ )

$\sigma$ is the uniform surface charge density of a thin spherical shell of radius ${\text{R}}$. The electric field at any point on the surface of the spherical shell is :

An electric charge $10^{-6} \mu {\text{C}}$ is placed at origin $(0,0)$ ${\text{m}}$ of ${\text{X}}- {\text{Y}}$ co-ordinate system. Two points ${\text{P}}$ and ${\text{Q}}$ are situated at $({\sqrt{3}}, {\sqrt{3}}) {\text{m}}$ and $({\sqrt{6}}, 0) {\text{m}}$ respectively. The potential difference between the points ${\text{P}}$ and ${\text{Q}}$ will be : [27-Jan-2024 Shift 1]

Five charges $+q,+5 q,-2 q,+3 q$ and $-4 q$ are situated as shown in the figure. The electric flux due to this configuration through the surface $S$ is :

If the net electric field at point ${\text{P}}$ along ${\text{Y}}$ axis is zero, then the ratio of ${| \;\frac{q_2}{q_3} |}$ is $\;{8}/{5 {\sqrt{x}}}$,where ${\text{x}}=$ ______.

Suppose a uniformly charged wall provides a uniform electric field of $2 \times 10^4 {\text{N}} / {\text{C}}$ 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 $\;{1}/{\sqrt{ {\text{x}}}} \mu {\text{C}}$ where $x=. . . . [.$ use $g=10 {\text{m}} / {\ s}^2]$ [1-Feb-2024 Shift 2]

Two charged conducting spheres of radii $a$ and $b$ are connected to each other by a conducting wire. The ratio of charges of the two spheres respectively is:

An infinitely long positively charged straight thread has a linear charge density $\lambda {\text{Cm}}^{-1}$. An electron revolves along a circular path having axis along the length of the wire. The graph that correctly represents the variation of the kinetic energy of electron as a function of radius of circular path from the wire is :

Two identical conducting spheres ${\text{P}}$ and ${\text{S}}$ with charge ${\text{Q}}$ on each, repel each other with a force $16 {\text{N}}$. A third identical uncharged conducting sphere ${\text{R}}$ is successively brought in contact with the two spheres. The new force of repulsion between ${\text{P}}$ and ${\text{S}}$ is :

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, $\;\frac{1}{4 \pi E_0}=9 \times 10^9 {\text{SI}}$ units) [27-Jan-2024 Shift 1]

At the centre of a half ring of radius $R=10 {\text{cm}}$ and linear charge density $4 {\text{n}} \; \text{C}{\text{m}}^{-1}$, the potential is $x \pi V$. The value of $x$ is _____

The distance between charges $+ {\text{q}}$ and $- {\text{q}}$ is $2 l$ and between $+2 {\text{q}}$ and $-2 {\text{q}}$ is $4 l$. The electrostatic potential at point ${\text{P}}$ at a distance ${\text{r}}$ from centre ${\text{O}}$ is -\alpha \[;\frac{q l}{r^2}]$ \times 10^9 {\text{V}}$, where the value of$\alpha $is (Use$;\frac{1}{4 \pi \epsilon _0}=9 \times 10^9 {\text{Nm}}^2 {\text{C}}^{-2})$ [31-Jan-2024 Shift 2]

Two identical charged spheres are suspended by string of equal lengths. The string make an angle of $37^{\circ}$ with each other. When suspended in a liquid of density $0.7 {\text{g}} / {\text{cm}}^3$, the angle remains same. If density of material of the sphere is $1.4 {\text{g}} / {\text{cm}}^3$, the dielectric constant of the liquid is ______$(\tan 37^{\circ}=\;\frac{3}{4})$. [30-Jan-2024 Shift 2]

An electric field, $\vec{E}=\;{2 \hat{i}+6 \hat{j}+8 \hat{k}}/{{\sqrt{6}}}$ passes through the surface of $4 {\text{m}}^2$ area having unit vector $\hat{n}= (\;{2 \hat{i}+\hat{j}+\hat{k}}/{{\sqrt{6}}})$. The electric flux for that surface is _______ ${\text{V}} {\text{m}}$.

A charge $q$ is placed at the center of one of the surface of a cube. The flux linked with the cube is :-

The electrostatic potential due to an electric dipole at a distance ' $r$ ' varies as : [30-Jan-2024 Shift 1]

An infinite plane sheet of charge having uniform surface charge density $+\sigma _{ {\ s}} {\text{C}} / {\text{m}}^2$ is placed on ${\text{x}}- {\text{y}}$ plane. Another infinitely long line charge having uniform linear charge density $+\lambda _e {\text{C}} / {\text{m}}$ is placed at ${\text{z}}=4 {\text{m}}$ plane and parallel to ${\text{y}}$-axis. If the magnitude values ${| \sigma _{ {\ s}} |}=2{| \lambda _{ {\text{e}}} |}$ then at point $(0,0,2)$, the ratio of magnitudes of electric field values due to sheet charge to that of line charge is $\pi \sqrt{ {\text{n}}}: 1$. The value of $n$ is ________

Given below are two statements : one is labelled aAssertion (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 : [27-Jan-2024 Shift 2]