The electric field in a certain region is acting radially outward and is given by $E = Ar$. $A$ charge contained in a sphere of radius $a$ centered at the origin of the field will be given by:

The electric field in a region is radially outward and at a point is given by $E = 250 r \, V/m$ (where $r$ is the distance of the point from the origin). Calculate the charge contained in a sphere of radius $20 \, cm$ centered at the origin in Coulombs $(C)$.

$A$ solid sphere of radius $R$ has a charge $Q$ distributed in its volume with a charge density $\rho = \kappa r^a$,where $\kappa$ 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 that at $r = R$,find the value of $a$.

An infinite line charge produces a field of $9 \times 10^4 \ NC^{-1}$ at a distance of $2 \ cm$. Its linear charge density is

The electric field inside a spherical shell of uniform surface charge density is

The electric field at a distance of $20 \ cm$ from the center of a charged spherical shell of radius $10 \ cm$ is $100 \ V/m$. What is the electric field at a distance of $3 \ cm$ from the center?