A uniformly charged non-conducting solid sphere has a total positive charge of $16 \mu\mathrm{C}$ an

Question

A uniformly charged non-conducting solid sphere has a total positive charge of $16 \mu\mathrm{C}$ and a radius of $4 \mathrm{~m}$. What is the magnitude of the electric field at a distance of $1 \mathrm{~m}$ from its centre?

Professor PC Thomas Classes · Answer

(a) : For a solid non-conducting sphere, the electric field inside ($r < R$) is given by $E = \frac{1}{4\pi\varepsilon_0} \frac{Qr}{R^3}$. Given $Q = 16 \mu\mathrm{C} = 16 	imes 10^{-6} \mathrm{C}$, $R = 4 \mathrm{~m}$, and $r = 1 \mathrm{~m}$. Thus, $E = (9 	imes 10^9) 	imes \frac{16 	imes 10^{-6} 	imes 1}{4^3} = 9 	imes 10^9 	imes \frac{16 	imes 10^{-6}}{64} = 9 	imes 10^3 	imes \frac{1}{4} = 2250 \mathrm{~N/C}$.