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. Determine the tension in the string in equilibrium.

Step-by-step solution

In equilibrium, the forces acting on the small ball are the weight of the ball mg acting vertically downwards, the electric force qE acting horizontally, and the tension T in the silk thread acting along the thread. Resolving the tension T into vertical and horizontal components gives T and T respectively. For vertical equilibrium, the vertical component of tension balances the weight of the ball: T = mg Substituting the given values m = 10 g = 0.01 kg , g = 10 m/s ^2 , and = 60^ : T 60^ = 0.01 10 T 1 2 = 0.1 T = 0