A ring of radius $1 \mathrm{m}$ is placed in an uniform electric field such that the electric flux through it is maximum. If the maximum flux is $2\times {10}^4 {\mathrm{Nm}}^2/\mathrm{C}$, what is the intensity of the electric field? 

(1) when the surface is parallel to $YZ$ -plane.

Find the electric flux through the surface in the following cases:

An uniform electric field of intensity $6\times {10}^3 \mathrm{N}/\mathrm{C}$ is directed along, $X$ -axis. The length and breadth of a rectangular plane surface is $1 \mathrm{m}$ and $0.5 \mathrm{m}$ respectively.

(ii) When the surface is parallel to $XY$ -plane.

(c) the length of the surface is parallel to $Y$-axis, but the normal drawn to it is inclined to the $X$ -axis at an angle of ${60}^{°}$.

A small metal sphere carrying charge $+Q$ is located at the centre of a spherical cavity in a large uncharged metal sphere as shown in the figure, Fig. $3.72$. Use Gauss's law to find electric field at points $P_1$ and $P_2$.

(ii) If the radius of the Gaussian surface is doubled, how would the flux change?