Question

1-The figure below shows two identical (and small) conducting spheres connected to each other by a string of length L = 3.0 meters.

Presently the charge on each small sphere is Q = +0.4 mC, and the string will break when the tension in the string equals or exceeds 1000N. A charge q is now placed on the small sphere on the right. If the string connecting the two spheres is conducting, determine the minimum value of q so that the string breaks.

2- Consider the same scenario as in problem #1 above but this time a charge q is placed on the small sphere on the right and the string connecting the two spheres is non-conducting, determine the minimum value of q so that the string breaks.

Answer 1

If the string is conducting then charges will distribute equally on two spheres as they are identical

q₁ = Q + q/2

q₂ = Q + q/2 =q₁

L = 3m

Q = 0.4 mC = 0.4 X 10^-3 C

The force between two charges will be

This force must be equal to 1000 N in order to break the string

q₁² = 10^-6

q ₁ = 10^-3 C = 1 mC

Q + q/2 = 1

q/2 = 1 -Q = 1- 0.4

q/2 = 0.6

q = 1.2 mC

b) the string is non - conducting

q₁ = Q

q₂ = Q + q

L = 3m

The force between two charges will be

This force must be equal to 1000 N in order to break the string

10^-6 = Q(Q+q)

10^-6 = 0.4 X 10^-3 ( 0.4 X 10^-3 + q)

2.5 X 10^-3 = 0.4 X 10^-3 + q

q = 2.1 mC