$A$ charged ball $B$ hangs from a silk thread $S$,which makes an angle $\theta$ with a large charged conducting sheet $P$,as shown in the figure. The surface charge density $\sigma$ of the sheet is proportional to

If a charge $q$ is placed on one of the vertices of a cube,then the flux passing through any one face of the cube is . . . . . . .

$A$ spherically symmetric charge distribution is characterized by a charge density $\rho(r) = \rho_0 \left( \frac{5}{4} - \frac{r}{R} \right)$ for $r \le R$ and $\rho(r) = 0$ for $r > R$,where $r$ is the distance from the origin. The electric field at a distance $r$ from the origin $(r < R)$ is given by:

The charge density of a solid sphere of radius $R$ and total charge $Q$ is given by $\rho(r) = \frac{Q}{\pi R^4} r$. The value of the electric field at a point $P$ inside the sphere at a distance $r_1$ from the center is .......

Two large,thin metal plates are parallel and close to each other. On their inner faces,the plates have surface charge densities of opposite signs and of magnitude $17.0 \times 10^{-22} \; C/m^2$. What is $E$:
$(a)$ in the outer region of the first plate,
$(b)$ in the outer region of the second plate,and
$(c)$ between the plates?

The electric field at a distance $r$ from the centre in the space between two concentric metallic spherical shells of radii $r_1$ and $r_2$ carrying charges $Q_1$ and $Q_2$ respectively is $(r_1 < r < r_2)$.