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 × 10³ N/C 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,

Where, q = Net charge = 1.5 × 10³ N/C
d = Distance from the centre = 20 cm = 0.2 m
ε_o = Permittivity of free space and 1/4πε_o=9×10⁹ Nm²C⁻²
Therefore,

q=E(4πε_o)d²=1.5×10³/9×10⁹
= 6.67 × 10⁹ C
= 6.67 nC

Therefore, the net charge on the sphere is 6.67 nC.