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.