An infinite non-conducting sheet has a surface charge density $\sigma = 0.10 \, \mu C/m^2$ on one side. How far apart are equipotential surfaces whose potentials differ by $50 \, V$?

Three infinitely long charged sheets are placed as shown in the figure. The electric force acting on a charge $-q$ placed at the point $P$ is ($\sigma=$ surface charge density,$\varepsilon_0=$ permittivity of free space).

In a cuboid of dimension $2 L \times 2 L \times L$,a charge $q$ is placed at the centre of the surface ' $S$ ' having an area of $4 L^2$. The flux through the opposite surface to ' $S$ ' is given by

Three infinitely long charged thin sheets are placed as shown in the figure. The magnitude of the electric field at point $P$ is $\frac{x \sigma}{\epsilon_0}$. The value of $x$ is . . . . . . . (All quantities are measured in $SI$ units).

$A$ non-conducting solid sphere of radius $R$ is uniformly charged. The magnitude of the electric field due to the sphere at a distance $r$ from its center is:
$(1) \text{ Increases with increase in } r \text{ for } r < R$
$(2) \text{ Decreases with increase in } r \text{ for } 0 < r < \infty$
$(3) \text{ Decreases with increase in } r \text{ for } R < r < \infty$
$(4) \text{ Is continuous at } r = R$

The electric field in a region is radially outward with magnitude $E = A r_0$. The charge contained in a sphere of radius $r_0$ centered at the origin is