$A$ 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 $..... \times 10^{-11} \, C$.

Electric field at a point varies as $r^0$ for

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:

Gauss's law can help in the easy calculation of the electric field due to:

$A$ non-conducting solid sphere of radius $R$ is uniformly charged. The magnitude of the electric field due to the sphere at a distance $r$ from its center is:
$(1) \text{ Increases with increase in } r \text{ for } r < R$
$(2) \text{ Decreases with increase in } r \text{ for } 0 < r < \infty$
$(3) \text{ Decreases with increase in } r \text{ for } R < r < \infty$
$(4) \text{ Is continuous at } r = R$

$A$ hollow cylinder has a charge $q$ within it. If $\phi$ is the electric flux in units of $V-m$ associated with the curved surface $B,$ the flux linked with the plane surface $A$ in units of $V-m$ will be