Question

Given a circular disk of radius R = 0.4 m and containing uniformly distributed charge with surface charge density, $\sigma =1C/m^2$. The electric field at a point P which is 0.3m along the axis of the disc from the centre is $\frac{1}{n{\epsilon }_0}$ where n is a natural number whose value is equal to ___

Answer 1

Once you go through the derivation video of electric field due to a disc (or better if you derive it on your own!) you would know that electric field due to a disc

$|\overrightarrow{E}|=\frac{\sigma }{2{\epsilon }_0}(1-cos\theta )$

Here R = 0.4 m

and x = 0.3 m

Which implies $cos\theta =\frac{0.3}{0.5}=\frac{3}{5}$

Now $|\overrightarrow{E}|=\frac{1}{2{\epsilon }_0}(1–\frac{3}{5})$

$=\frac{1}{2{\epsilon }_0}\left(\frac{2}{5}\right)=\frac{1}{5{\epsilon }_0}$

So we see that n = 5