Question

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

Answer 1

$\text{Step 1: Electric field outside a conducting sphere}$

$E=\frac{1}{4\pi {\in }_0}\frac{q}{r^2}$

where $r$ is the distance from the centre of conducting sphere.

$\therefore q=4\pi {\in }_{0}E{r}^2$ $....\left(1\right)$

$\text{Step 2: Substituting the values}$

$q=\frac{1}{9\times {10}^9}\times 1.5\times {10}^{3}N/C\times (0.2m{)}^2$$=6.67\times {10}^{-9}C=6.67nC$

Because the electric field lines point radially inwards, the nature of the charge on the sphere is negative.

Therefore $q=-6.67nC$