One end of a silk thread of length 10 cm is attached to the large vertical surface of a charged nonconducting plate. The thread's opposite end is tied to a small ball having a mass of 10 g and a charge of 4.0 10⁻⁶ C . In equilibrium, the thread forms an angle of 60^ with the vertical. If the ball is slightly pushed aside and released, determine the time period of the small oscillations.

Step-by-step solution

In equilibrium, the forces acting on the ball are the tension in the thread T , the gravitational force mg , and the horizontal electric force qE . From the equilibrium condition, the effective acceleration due to gravity g_ eff is the vector sum of the acceleration due to gravity g and the acceleration due to the electric field qE m . The angle made by the thread with the vertical is = 60^ . The effective gravity is given by: g_ eff = g = g 60^ = 2g The time period of small oscillations for the pendulum is: T = 2