An unknown charge sits on a conducting solid sphere of radius 9.0 cm. If the electric field 14 cm from the center of the sphere has magnitude 2.7 103 N/C and is directed radially inward, what is the net charge on the sphere?

The net charge on the sphere is - 5.9 × 10⁻⁹ C = - 5.9 nC

Explanation:

The electric field (E) produced by a charge of magnitude Q, at a point with distance r away from the charge, is given by

E = kQ/r²

where k = Coulomb's constant = 9.0 x 10⁹ Nm²/C²

The electric field 14 cm (0.14 m) from the sphere is 2.7 × 10³ N/C

2.7 × 10³ = 9.0 x 10⁹ × Q/(0.14²)

Q = (2.7 × 10³ × 0.14²)/(9.0 x 10⁹) = 5.9 × 10⁻⁹ C

Since the charge is directed inwards towards the centre of the sphere, the sign on it will be -ve. Q = - 5.9 × 10⁻⁹ C

b) The electric field 9 cm (0.09 m) from the sphere will be

E = kQ/(0.09²) = (9 × 10⁹ × 5.9 × 10⁻⁹)/(0.09²) = 6555.56 = 6.56 × 10³ N/C