What will be the total electric flux through the faces of a cube of side length $a$ if a charge $q$ is placed at:
$(a)$ $A$: a corner of the cube.
$(b)$ $B$: the midpoint of an edge of the cube.

The electric field in a certain region is acting radially outward and is given by $E = Ar$. $A$ charge contained in a sphere of radius $a$ centered at the origin of the field will be given by:

According to Gauss's Theorem,the electric field of an infinitely long straight wire is proportional to

Two concentric shells of radii $R$ and $3R$ are placed as shown in the figure. The outer shell carries a charge $Q$. The inner shell is grounded. Find the electric field at point $P$,which is at a distance $2R$ from the center.

This question has Statement-$1$ and Statement-$2$. Of the four choices given after the statements,choose the one that best describes the two statements.
An insulating solid sphere of radius $R$ has a uniformly positive charge density $\rho$. As a result of this uniform charge distribution,there is a finite value of electric potential at the centre of the sphere,at the surface of the sphere,and also at a point outside the sphere. The electric potential at infinity is zero.
Statement-$1$: When a charge $q$ is taken from the centre to the surface of the sphere,its potential energy changes by $\frac{q \rho R^2}{6 \epsilon_0}$.
Statement-$2$: The electric field at a distance $r (r < R)$ from the centre of the sphere is $\frac{\rho r}{3 \epsilon_0}$.

Two infinitely long parallel wires having linear charge densities $\lambda_1$ and $\lambda_2$ respectively are placed at a distance of $R$ meters. The force per unit length on either wire will be $(K = \frac{1}{4\pi\varepsilon_0})$.