A conducting sphere of radius $10 ext{ cm}$ has an unknown charge. If the electric field $20 ext{

Question

A conducting sphere of radius $10	ext{ cm}$ has an unknown charge. If the electric field $20	ext{ cm}$ from the centre of the sphere is $1.5 	imes 10^3	ext{ N/C}$ and points radially inward, what is the net charge on the sphere?

Professor PC Thomas Classes · Answer

For a point outside a conducting sphere, $E = \frac{1}{4\pi\epsilon_0} \frac{Q}{r^2}$. Because it points inward, $Q$ is negative. $|Q| = \frac{E r^2}{k} = \frac{1.5 	imes 10^3 	imes (0.2)^2}{9 	imes 10^9} = \frac{60}{9 	imes 10^9} = 6.67 	imes 10^{-9}	ext{ C}$. Thus, $Q = -6.67	ext{ nC}$.