Gauss's Law

Explain in which condition the charge of a conductor is totally transferred to another conductor.

From Gauss's law find the outward pressure acting on the surface of a charged conductor.

Explain why the inverse square law is essential for Gauss's law to hold.

Obtain Coulomb's law from Gauss's law. Indicate the additional information you require for their derivation.

Derive Gauss's law from Coulomb's law.

If a Gaussian surface does not include any charge, does it necessarily mean that electric field is zero at all points on the surface.

Explain why Gauss's law cannot be used to calculate the electric field of three-point charges at the corners of a triangle.

Explain why Gauss's law cannot be used to calculate the electric field of a charged disc.

Explain why Gauss's law cannot be used to calculate the electric field of an electric dipole.

Number of field lines entering a Gaussian surface is less than the number of field lines emerging from it. What it implies?

State Gauss's law.

Find the electrostatic potential at a point $P$ at a distance $\frac{R}{2}$ from the centre of the shell is, when a thin spherical conducting shell of radius $R$ has a charge $q$. Another charge $Q$ is placed at the centre of the shell.

A solid sphere of radius $R$ has a charge $Q$ distributed in its volume with a charge density $\rho =k{r}^a,$ where $k$ and $a$ constants and $r$ is the distance from its centre. If the electric field at $\frac{R}{2}$ is $\frac{1}{8}$ times that at $r=R,$ find the value of $a.$

The electrostatic potential inside a charged spherical ball is given by $\varphi =a{r}^2+b$ where $r$ is the distance from the centre, $a$ and $b$ are constants. Then the charge density inside the ball is

A cylinder of radius $r$ and length $l$ is placed on an uniform electric field $E$ parallel to the axis of the cylinder. The total flux for the surface of the cylinder is given by

There are two identical parallel metal plates $A$ and $B$ facing each other. Charge $q$ is given to the plate $A.$ Find the charges residing on the outer and inner (facing) surface of the two plates.

An infinite wire having line charge density $\lambda$ passes through one edge of cube having edges of length $a.$ Find the flux passing through the surfaces which are in contact with the wire.

An infinite wire having line charge density $\lambda$ passes through one edge of cube having edges of length $a.$ Find the flux passing through the surface which are is constant with the wire,

A solid sphere of radius $R$ has a charge $Q$ distributed in its volume with a charge density $\rho =k{r}^a,$ where $k$ and $a$ are constants and $r$ is the distance from its centre. If the electric field at $r=\frac{R}{2}$ is $\frac{1}{8}$ times at $r=R,$ find the value of $a.$

What is a Gaussian surface?