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

Charges $Q, 2Q$ and $4Q$ are uniformly distributed in three dielectric solid spheres $1, 2$ and $3$ of radii $R/2, R$ and $2R$ respectively,as shown in the figure. If magnitudes of the electric fields at point $P$ at a distance $R$ from the centre of spheres $1, 2$ and $3$ are $E_1, E_2$ and $E_3$ respectively,then:

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 . . . . . . .

Let $\sigma$ be the uniform surface charge density of two infinite thin plane sheets shown in the figure. Then the electric fields in three different regions $I, II$ and $III$ are:

Two concentric conducting thin spherical shells $A$ and $B$ having radii $r_A$ and $r_B$ $(r_B > r_A)$ are charged to $Q_A$ and $-Q_B$ $(|Q_B| > |Q_A|)$. The electric field along a line passing through the centre is:

$A$ hollow insulated conducting sphere is given a positive charge of $10\,\mu C$. What will be the electric field at the centre of the sphere if its radius is $2\,m$?