Question

Calculate electric field intensity due to a spherical charge distribution given as ρ(x)=ρ°{1-(x²/R²)} , x≤R

And ρ(x)=0; x>R at external point, at surface and at internal point.

Answer 1

$\rho=dq/dV\to q(x)=\int\rho dV=4\pi\rho_0(x^3/3-x^5/(5R^2))$

$\int EdA=q/\epsilon_0$ . So, we have

$E=(\rho_0/\epsilon_0)\cdot(x/3-x^3/(5R^2))\ \ \ x\leq R$

$E=(\rho_0/\epsilon_0)(2R^3/(15x^2))\ \ \ x> R$