Two charge spheres 10 cm apart attract each other with a force of 3 µN. What force results from each of the following changes,considered separately?
a) Both charges are doubled and the distance remains the same.
b) An uncharged, identical sphere is touched to one of the spheres, and then taken away.
c) The separation is increased to 30 cm.
Electrostatic Force, F = k.q1.q2 /r 2 , where k = 1/ 4π ε0
(a) When q1q2 => 2 q1 * 2 q2 = 4 q1q2
=> F' = k * 4 * q1.q2 /r 2
=> F' = 4F = 4 * 3 = 12 N
(b) When an uncharged sphere is kept in contact with the charged sphere, the charge is equally distributed throughout the spheres in contact. Thus, one of charges, say q1 gets halved. ie, q1 => (q1)/2
Thus,
=> F" = k .{(q1)/2}.q2 /r 2
=> F" = F/2 = 3/2 N
(c) When r = 30 cm
F"' = k.q1.q2 /(30) 2
=> F'" = k.q1.q2 /(3*10) 2
=> F'" = k.q1.q2 /(9 * r2)
=> F"' = F/9N