The intensity of an electric field depends only on the coordinates and as follows: E…

PHYSICS · Subjective · A Level · Physics · Fields and their consequences · Fields and their consequences

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 unit vectors along the

x

- and

y

-axes. Find the charge within a sphere of radius

r

centred at the origin.