Find the ratio of the electric field at points $A$ and $B$. An infinitely long uniformly charged wire with linear charge density $\lambda$ is kept along the $z$-axis.

$A$ thin metallic spherical shell of radius $r$ contains a charge $Q$ on its surface. $A$ point charge $q_1$ is placed at the centre of the shell and another charge $q_2$ is placed outside the shell at a distance $x$ from the centre. Then, the forces on charges $q_1$ and $q_2$ respectively are

Obtain the expression for the electric field due to a straight wire of infinite length with a linear charge density $\lambda$.

There is a solid sphere of radius $R$ having uniformly distributed charge throughout it. What is the relation between electric field $E$ and distance $r$ from the centre (where $r < R$)?

$A$ very long charged solid cylinder of radius 'a' contains a uniform charge density $\rho$. The dielectric constant of the material of the cylinder is $k$. What will be the magnitude of the electric field at a radial distance '$x$' $(x < a)$ from the axis of the cylinder?

An infinite sheet carrying a uniform surface charge density $\sigma$ lies on the $xy$-plane. The work done to carry a charge $q$ from the point $A = a(\hat{i} + 2\hat{j} + 3\hat{k})$ to the point $B = a(\hat{i} - 2\hat{j} + 6\hat{k})$ (where $a$ is a constant with the dimension of length and $\varepsilon_{0}$ is the permittivity of free space) is