Q.A thin spherical shell of radius $10\ \text{cm}$ carries a total charge of $2\ \mu\text{C}$ uniformly spread over its surface. Using Gauss's theorem, find the electric field

Shell radius $R=10\ \text{cm}=0.1\ \text{m}$, total charge $Q=2\ \mu\text{C}=2\times10^{-6}\ \text{C}$.

(a) At $r=5\ \text{cm}=0.05\ \text{m}$, since $r<R$, this point lies INSIDE the shell. A concentric Gaussian sphere of this radius encloses no charge (all the shell's charge sits on its surface, at $r=R>0.05\ \text{m}$), so

$E = 0$ …

Compare $r$ to $R$ first to decide which of the two Gauss's-theorem cases applies, then use $E=0$ (i …

• Using $E=kQ/r^2$ for the inside point as well (a common error -- the field is exactly zero inside a uniformly charged SHELL, unlike inside a uniformly charged SOLID sphere, which is a different, more advanced case). …