If the potential at the centre of a uniformly charged hollow sphere of radius $R$ is $V$,then the electric field at a distance $r$ from the centre of the sphere is $(r > R)$.

When a $5 C$ charge is kept in a uniform electric field,a force of $5000 N$ acts on it. Find the potential difference between two points in that field,separated by a distance of $1 cm$. (in $V$)

Two charges $+5\,\mu C$ and $+10\,\mu C$ are placed $20\,cm$ apart. The net electric field at the midpoint between the two charges is

Consider the following statements about electric field intensity and electric potential.
$A$. The electric field intensity due to a charged spherical shell is inversely proportional to the square of its distance from the center for points outside the shell.
$B$. The electric potential due to a point charge is inversely proportional to the distance between the charge and the point.

Obtain the equation of electric field at a point due to a system of $n$ point charges.

The charge distribution along the semi-circular arc is non-uniform. The charge per unit length $\lambda$ is given as $\lambda = \lambda_0 \sin \theta$,with $\theta$ measured as shown in the figure. $\lambda_0$ is a positive constant. The radius of the arc is $R$. The electric field at the center $P$ of the semi-circular arc is $E_1$. The value of $\frac{\lambda_0}{\epsilon_0 E_1 R}$ is