The ratio of electric field on the equatorial point and at the axial point at equal distances from the centre of a short electric dipole is ______.

A spherical shell of radius $\mathrm{R}$ is uniformly charged with charge $+\mathrm{q}$. By Gauss's theorem, find the electric field intensity at a point $\mathrm{p}$. Outside the spherical shell.

A spherical shell of radius $\mathrm{R}$ is uniformly charged with charge $+\mathrm{q}$. By Gauss's theorem, find the electric field intensity at a point $\mathrm{p}$.

Inside the spherical shell.

A permanent electric dipole of dipole moment $\mathrm{p}$is placed in a uniform external electric field $\mathrm{E}$, as shown in Figure.

Redraw the figure and show the magnitude and direction of force acting on the charges.

An infinitely long thin straight wire with uniform linear charge density is shown in figure.

Draw a Gaussian surface in order to calculate the electric direction field at $\mathrm{P}$ and mark direction of electric field at this point.

An infinitely long thin straight wire with uniform linear charge density is shown in figure.

$\left(\mathrm{b}\right)$ Derive an expression to calculate electric field at this point $\mathrm{P}$.