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?

Answer: The net charge on the sphere is - 5.9nC

Explanation:

The electric field outside the conducting solid sphere is given as:

E = (kq) / r^2

Here, q is the net charge on the sphere and r is the distance from the center of the sphere.

The net charge is calculated as follows;

q = Er^2/k

E = 2.7*10^3N/C

r = 14cm = 0.14m

k = 8.99*10^9Nm^2/C^2

q = (2.7*10^3) (0.14^2) / (8.99*10^9)

q = 5.9*10^-9C

= 5.9nC

As the electric field directed radially inward, the net charge on the sphere is negative.

Hence the net charge on the sphere is - 5.9nC