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?

Given:

Radius of charged sphere, r = 10 cm

Electric field, 20 cm away from centre of sphere, E = 1.5 × 10³ NC^-1

We know that, electric field intensity at a point P, located at a distance R, due to net charge q is given by,

…(1)

Now plugging the values of q and R in equation (1)

q = 4 × π × ε₀ × R² × E

⇒ q = 4 × 3.14 × 8.85 × 10^-12N^-1m^-2C^-2 × (0.2m)² × 1.5 × 10³C

⇒ q = 6.67 × 10^-9C

The net charge on the sphere is -6.67 × 10^-9C. Since the electric field points radially inwards, we can infer that charges on sphere are negative.