Problem

The intensity of an electric field depends only on the coordinates

x

and

y

as follows

\mathbf{E} = \frac{a (x \hat{i} + y \hat{j})}{x^2 + y^2}

where,

a

is a constant and

\hat{i}

and

\hat{j}

are the unit vectors of the

x

and

y

-axes. Find the charge within a sphere of radius

R

with the centre at the origin.