Observe the setup illustrated in the figure. The work performed in moving a point charge from P to A is W_A , from P to B is W_B , and from P to C is W_C .

Step-by-step solution

Points A , B , and C lie on a circular arc with the point charge q at its center. Therefore, the distances from the charge q to points A , B , and C are equal to the radius r . The electric potential V at a distance r from a point charge q is V = 1 4 ₀ q r . Since the distances are equal, the electric potentials at points A , B , and C are the same: V_A = V_B = V_C The work done W in moving a test charge Q from point P to a point X is W_X = Q(V_X - V_P) . Because V_A = V_B = V_C , the work done is equal for all thr