Question

1 Sphere illed with charge Te Consider a sphere ith radivs Ba outside and inside t sphera (Inside) le th cha constant Coufsi

Answer 1

Radius of charged solid sphere= R

Electric charge on sphere: Q = ρV = 4πρR^3/3.

Use a concentric Gaussian sphere of radius r.

For r > R:

$E(4\pi r^2)=Q/\varepsilon _0\\ \\ \Rightarrow E=\frac{Q}{4\pi \varepsilon _0 r^2}$

For r < R:

$E(4\pi r^2)=\frac{1}{\varepsilon _0}\left ( \frac{4\pi}{3} r^3\rho \right ) \\ \Rightarrow E=\frac{\rho}{3 \varepsilon _0 }r =\frac{1}{4\pi \varepsilon_0}\frac{Q}{R^3}r$