There is a solid sphere of radius $R$ having uniformly distributed charge throughout it. What is the relation between electric field $E$ and distance $r$ from the centre (where $r < R$)?

Two infinitely long thin straight parallel wires are kept at a perpendicular distance of $2R$,having uniform linear charge densities $+\lambda$ and $-\lambda$ respectively. The magnitude of the electric field at the midpoint between the two wires will be . . . . . . .

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).

The line $AA^{\prime}$ lies on a charged infinite conducting plane which is perpendicular to the plane of the paper. The plane has a surface charge density $\sigma$. $B$ is a ball of mass $m$ with a like charge of magnitude $q$. $B$ is connected by a string to a point on the line $AA^{\prime}$. The tangent of the angle $\theta$ formed between the line $AA^{\prime}$ and the string is:

$A$ non-conducting solid sphere of radius $R$ has a uniform volume charge density $\rho$. The electric potential at the center of the sphere is related to the potential at the surface and outside the sphere due to this uniform charge distribution.
Statement-$1$: When a charge $q$ is moved from the surface to the center of the sphere,the change in its potential energy is $q\rho R^2 / 6\varepsilon_0$.
Statement-$2$: The electric field at a distance $r$ $(r < R)$ from the center of the sphere is $\rho r / 3\varepsilon_0$.

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