Question

Two small nonconducting spheres have a total charge of 90.0 µC.

(a) When placed 1.06 m apart, the force each exerts on the otheris 12.0 N and is repulsive.
I) What is the charge on each?
a) smaller charge is .........Coulombs
b) larger ........Coulombs
II) What if the force were attractive?
c) smaller ..........Coulombs
d) larger ..........Coulombs

Answer 1

(a) Force is repulsive means both the spheres have same charge.

The total charge on the two non-conducting sphere is.

Q1 + Q2 = 9*10^-5 C

The force between the two spheres is,

F = k * (Q1 * Q2) / r^2

Q1Q2 = 1.5x10^-9

Q1(9*10^-5-Q1) = 1.5x10^-9

On solving this quadratic we get,

Smaller charge as 2.21x10^-5 C

Larger charge as 6.79x10^-5 C

(b) Smaller charge is -1.44x10^-5 C

Larger charge is 1.04x10^-4 C