Question

6. A particle having a mass of 1.0 g and a charge of +2.0 μC is attached to the center of a uniformly positively charged insulating sheet 100 cm on a side by a thread of negligible mass that is 1 cm in length. The particle is displaced slightly from equilibrium and oscillates with a period of 10 ms, what is the charge on the plate? Ignore gravitational effects.

Answer 1

Let charge on plate be Time period T = 2 pi squareroot l/a a = F/m = q epsilon/m T = 2 pi squareroot lm/q epsilon where E = sigma/z epsilon_0 = Q/2 epsilon_0 a^2 T^2 = e pi^2 lm/q Q 2 epsilon_0 a^2 [1/4 pi epsilon_0 = 9 times 10^9 Q = 4 pi^2 lm z epsilon_0 a^2/2 T^2 = (4 pi epsilon_0) pi ln times 2a^2/q T^2 Q = pi times 10^-2 times 10^-3 times 2 times 1^2/2 times 10^-6 times (10 times 10^-3)^2 times 9 times 10^9 = pi/9 times 10^-4 c Q = 34.9 mu c