$A$ cube is placed inside an electric field,$\overrightarrow{E} = 150 y^2 \hat{j}$. The side of the cube is $0.5 \, m$ and it is placed in the field as shown in the figure. The charge inside the cube is $..... \times 10^{-11} \, C$.

Three infinite plane sheets carrying uniform charge densities $-\sigma, 2 \sigma, 4 \sigma$ are placed parallel to the $XZ$ plane at $Y=a, 3a, 4a$ respectively. The electric field at the point $(0, 2a, 0)$ is

$A$ non-conducting solid sphere has radius $R$ and uniform charge density. $A$ spherical cavity of radius $\frac{R}{4}$ is hollowed out of the sphere. The distance between the center of the sphere and the center of the cavity is $\frac{R}{2}$. If the charge of the sphere is $Q$ after the creation of the cavity and the magnitude of the electric field at the center of the cavity is $E = K \left( \frac{Q}{4 \pi \epsilon_0 R^2} \right)$,determine the approximate value of $K$.

What will be the total electric flux through the faces of the cube of side length '$a$' if a charge '$Q$' is placed at '$B$', the midpoint of an edge of the cube (see figure)?

The charge density of a uniformly charged infinite plane is $\sigma$. $A$ simple pendulum is suspended vertically downward near it. $A$ charge $q_0$ is placed on the metallic bob. If the angle made by the string with the vertical direction is $\theta$,then . . . . . . .

The electric potential in a region around the origin is given by $V(x) = 4x^2$. The total charge enclosed in a cube of side $1 \ m$ centered at the origin is (in Coulombs) ...