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 $1.5 × 10^3 NC^{-1}$ and points radially inward, what is the net charge on the sphere?

Answer 1

Electric field intensity (E) at a distance (d) from the centre of a sphere containing net charge q is given by the relation,
$E = \frac{1 }{ 4πε_0}.\frac {q}{d^2}$
Where, $q =$ Net charge = $1.5 × 10^3 NC^{-1}$
$d =$ Distance from the centre $= 20 cm = 0.2 m$
$ε_0$ = Permittivity of free space and $\frac{ 1 }{ 4 πε_0}$ = $9 × 10^9 Nm^2C^{-2}$
Therefore,
$q = E(4πε_0)d^2 = \frac{1.5 × 10^3 }{9 × 10^9}$
$= 6.67 × 10^9\,C$
$= 6.67 nC$
Therefore, the net charge on the sphere is 6.67 nC.