Question

A conducting sphere of radius 10cm has an unknown charge. If the electric field 20cm from the centre of the sphere is 1.5 x 10³N/C and the points radially inward, what is the net change on the sphere?

Answer 1

Consider a sphere of radius
R = (=10cm = 0.1 m) and centre O.
Let the charge on the sphere be ‘q’. Further, let ‘P’ be a point at a distance r = 20cm from the centre of the sphere.

The electric field E( = 1.5 x 10³NC^-1) is directed radially inward as shown. So as to enclose the charged sphere, draw a sphere (gaussian surface) with the point O as centre and r as the radius. As the electric field is radial, it is normal to the gaussian surface everywhere. Therefore, electric flux through the gaussian surface,

ϕ = -E x area of the gaussian surface

∴ ϕ = -E x 4πr²

= -1.5 x 10^-2 x 4π(0.2)²

According to Gauss's theorem,