Question

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

Answer 1

Let the value of unknown charge be q.
Electric field at 20 cm away E=$1.5\times {10}^{3}N/C\left(radiallyinwards\right)$
From the formula, electric field
$E=\frac{1}{4\pi {\epsilon }_0}.\frac{q}{r^2}(r=distance)1.5\times {10}^3=\frac{9\times {10}^9\times q}{(20\times {10}^{-2}{)}^2}q=\frac{1.5\times {10}^3\times 20\times 20\times {10}^{-4}}{9\times {10}^9}=6.67\times {10}^{-9}C$
As, the electric field is radially inwards which shows that the nature of unknown charge q is negative.