## Important Questions on Electrostatics

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Gauss’s Law

Two hollow concentric spheres $A$ and $B$ are enclosing electric charges $2\mathrm{C}$ and $8\mathrm{C}$ respectively. If the radius of $A$ is less than that of $B\mathit{,}$ the ratio of electric flux through $A$ to the electric flux through $B$ is

EASY

Physics>Electricity and Magnetism>Electrostatics>Gauss’s Law

A charge $Q$ is placed at a distance $\raisebox{1ex}{$a$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$ above the centre of a square surface of side length $a$. The electric flux through the square surface due to the charge would be?

EASY

Physics>Electricity and Magnetism>Electrostatics>Gauss’s Law

The number of electric lines that emerge from a finite charge $+q$is _____

EASY

Physics>Electricity and Magnetism>Electrostatics>Gauss’s Law

A charge$q$ is placed at the centre of a cube. The electric flux passing through the cube is

HARD

Physics>Electricity and Magnetism>Electrostatics>Gauss’s Law

The region between two concentric spheres of radii 'a' and 'b', respectively (see figure), has volume charge density $\mathrm{\rho}=\frac{\mathrm{A}}{\mathrm{r}}$ , where A is a constant and r is the distance from the centre. At the centre of the spheres is a point charge Q. The value of A such that the electric field in the region between the spheres will be constant, is:

HARD

Physics>Electricity and Magnetism>Electrostatics>Gauss’s Law

The potential due to an electrostatic charge distribution is $V\left(r\right)=\frac{q{e}^{-\alpha r}}{4\pi {\epsilon}_{0}r},$where $\alpha $ is positive. The net charge within a sphere centred at the origin and of radius $1/\alpha $ is

EASY

Physics>Electricity and Magnetism>Electrostatics>Gauss’s Law

Consider the force$\mathrm{F}$on a charge '$\mathrm{q}$' due to a uniformly charged spherical shell of radius$\mathrm{R}$carrying charge$\mathrm{Q}$distributed uniformly over it. Which one of the following statements is true for$\mathrm{F}$, if '$\mathrm{q}$' is placed at distance$\mathrm{r}$from the centre of the shell?

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Gauss’s Law

The following figure shows two point charges $+q$ and $-q$ and a metal rod of length $L$ carrying a charge $-q$with a part $\frac{L}{3}$ of its length inside a cubical box. The electric flux linked with the box will be,

HARD

Physics>Electricity and Magnetism>Electrostatics>Gauss’s Law

The potential (in volts) of a charge distribution is given by

$\mathrm{V}\left(\mathrm{z}\right)=30-5{\mathrm{z}}^{2}$ for $\left|\mathrm{z}\right|\le 1\mathrm{}\mathrm{m}$

$\mathrm{V}\left(\mathrm{z}\right)=35-10\mathrm{}\left|\mathrm{z}\right|$ for $\left|\mathrm{z}\right|\ge 1\mathrm{}\mathrm{m}$ .

$\mathrm{V}\left(\mathrm{z}\right)$ does not depend on x and y. If this potential is generated by a constant charge per unit volume ${\mathrm{\rho}}_{0}$ (in units of ${\mathrm{\u03f5}}_{0}$ ) which is spread over a certain region, then choose the correct statement.

HARD

Physics>Electricity and Magnetism>Electrostatics>Gauss’s Law

In finding the electric field using Gauss law the formula $\left|\overrightarrow{E}\right|=\frac{{q}_{\mathrm{e}\mathrm{n}\mathrm{c}}}{{\epsilon}_{0}\left|A\right|}$ is applicable. In the formula ${\epsilon}_{0}$ is permittivity of free space, $A$ is the area of Gaussian surface and ${q}_{\mathrm{e}\mathrm{n}\mathrm{c}}$ is charge enclosed by the Gaussian surface. This equation can be used in which of the following situation?

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Gauss’s Law

Given below are two statements

Statement $\mathrm{I}$: An electric dipole is placed at the centre of a hollow sphere. The flux of electric field through the sphere is zero, but the electric field is not zero anywhere in the sphere.

Statement $\mathrm{II}$: If $R$is the radius of a solid metallic sphere and $Q$be the total charge on it. The electric field at any point on the spherical surface of radius $r\left(<R\right)$ is zero but the electric flux passing through this closed spherical surface of radius $r$ is not

In the light of the above statements, choose the correct answer from the options given below:

EASY

Physics>Electricity and Magnetism>Electrostatics>Gauss’s Law

Shown in the figure are two point charges $+Q$ and $-Q$ inside the cavity of a spherical shell. The charges are kept near the surface of the cavity on opposite sides of the centre of the shell. If ${\sigma}_{1}$ is the surface charge on the inner surface and ${Q}_{1}$ net charge on it and ${\sigma}_{2}$ the surface charge on the outer surface and ${Q}_{2}$ net charge on it then:

EASY

Physics>Electricity and Magnetism>Electrostatics>Gauss’s Law

Arrangement of charges are shown in the figure. Flux linked with the closed surface $P$ and $Q$ respectivelyare ________and ________ .

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Gauss’s Law

Consider a region in free space bounded by the surfaces of an imaginary cube having sides of length $a$ as shown in the figure. A charge $+Q$ is placed at the centre $O$ of the cube. $P$ is such a point outside the cube that the line $OP$perpendicularly intersects the surface$ABCD$ at $R$ and also $OR=RP=a/2$. A charge $+Q$ is placed at point $P$ also. What is the total electric flux through the five faces of the cube other than $ABCD?$

EASY

Physics>Electricity and Magnetism>Electrostatics>Gauss’s Law

When a $10\mathit{}\mu \mathrm{C}$ charge is enclosed by a closed surface, the flux passing through the surface is $\mathrm{\varphi}.$ Now another $10\mu \mathrm{C}$charge is placed inside the closed surface, then the flux passing through the surface is _____

EASY

Physics>Electricity and Magnetism>Electrostatics>Gauss’s Law

Gauss's law helps in:

MEDIUM

Physics>Electricity and Magnetism>Electrostatics>Gauss’s Law

Choose the incorrect statement:

(a) The electric lines of force entering into a Gaussian surface provide negative flux.

(b) A charge $q$is placed at the centre of a cube. The flux through all the faces will be the same.

(c) In a uniform electric field net flux through a closed Gaussian surface containing no net charge, is zero.

(d) When an electric field is parallel to a Gaussian surface, it provides a finite non-zero flux.

Choose the most appropriate answer from the options given below:

EASY

Physics>Electricity and Magnetism>Electrostatics>Gauss’s Law

The electric flux (in $\mathrm{SI}$ units) through any face of a cube due to a positive charge $\mathrm{Q}$situated at the centre of a cube is

EASY

Physics>Electricity and Magnetism>Electrostatics>Gauss’s Law

If some charge is given to a solid metallic sphere, the field inside remains zero and by Gauss's law all the charge resides on the surface. Suppose now that Colomb's force between two charges varies as $\frac{1}{{\mathrm{r}}^{3}}.$ Then, for a charged solid metallic sphere

EASY

Physics>Electricity and Magnetism>Electrostatics>Gauss’s Law

A charge $+q$ is at a distance $\frac{L}{2}$ above a square of side $L$. Then what is the flux linked with the surface?