Question

Of the charge Q initially on a tiny sphere, a portion q is to be transferred to a second, nearby sphere. Both spheres can be treated as particles. For what value of q/Q>0.5 will the electrostatic force between the two parts have 1/3 of the maximum possible value?

Answer 1

Step-by-step explanation:

Maximum value of force will be possible when both the sphere will have same charge . In that case charge on each sphere = Q / 2 =.5Q

F( max ) = k .5Q x .5Q / R²

=.25kQ² /R²

For the second case

F = k q ( Q-q)/ R²

F = .25kQ² /3R²

.25kQ² /3R² = k q ( Q-q)/ R²

.25 Q² = 3qQ - 3q²

3q² - 3qQ + .25 Q² = 0

q =