Question

If electric field in a region is radially outward with magnitude E = Ar, the charge contained in a sphere of radius r centred at the origin is
(a) $\frac{1}{4\pi\epsilon_{0}}Ar^{2}$
(b) 4πε₀Ar³
(c) $\frac{1}{4\pi\epsilon_{0}}\frac{A}{r^{3}}$
(d) $\frac{4\pi\epsilon_{0}A}{r^{3}}$

Answer 1

From Gauss's law in electrostatics,

Ф = Q/ε

E A = Q/ε

Q = E A ε

Q = Ar (4Πr²)ε

Q = 4ΠεAr³

Option (b) is correct.