A silk thread 10 cm in length has one end attached to the large vertical surface of a charged nonconducting plate. The thread's other end is tied to a small ball with a mass of 10 g and a charge of 4.0 10⁻⁶ C . The thread forms an angle of 60^ with the vertical in equilibrium. Determine the surface charge density on the plate.

Step-by-step solution

Let T be the tension in the thread, E be the electric field due to the plate, m be the mass of the ball, and q be its charge. In equilibrium, the forces acting on the ball in the horizontal and vertical directions balance each other: T = qE T = mg Dividing the two equations, we get: = qE mg The electric field produced by a large nonconducting charged plate is given by E = 2 ₀ . Substituting this into the equation for : = q 2 ₀ mg Rearranging for : = 2 ₀ mg q Given values are m = 10 g = 10⁻² kg , q = 4.0 10⁻⁶ C , =