Question

An insulating sphere with radius a has a uniform charge density $\rho$. The sphere is not centered at the origin but at $r=b$. Find the electric field at any point inside sphere is $E=\frac{\rho (x-b)}{n{\epsilon }_0}$. what is the value of n

Answer 1

Using Gauss's law if E is the field inside sphere ,
$E.4\pi (x-b{)}^2=\frac{Q_{in}}{{ϵ}_0}=\frac{\rho .\left(4/3\right)\pi (x-b{)}^3}{{ϵ}_0}$
or $E=\frac{\rho (x-b)}{3{ϵ}_0}$