Question

Find an expression for the electric field in the region $r<a$

• A. $\frac{\rho r}{2{ϵ}_0}$
• B. $\frac{\rho r}{3{ϵ}_0}$
• C. $\frac{\rho r}{{ϵ}_0}$
• D. $\frac{2\rho r}{{ϵ}_0}$

Answer 1

The correct option is A $\frac{\rho r}{2{ϵ}_0}$

$p=\frac{q}{\pi a^{2}L}$

$r<a$

Electric field $=\frac{pr}{2{ϵ}_0}$

cylindrical electric field =

Now,

$E\times 2\pi aL=L\frac{q}{{ϵ}_0}$

or, $E\times 2\pi =0$

$E=\frac{1}{2\pi {ϵ}_0}\frac{1}{a^2}$

or, $E=\frac{q}{2\pi {ϵ}_0\times a^2}=\frac{pr}{2{ϵ}_0}$

$L=$ length

$a=$ radius