An electric dipole of length 2a is placed with its center at the origin. Let A and B be two points on the axial line at distances 2a and 3a respectively from the center of the dipole, both on the side of the positive charge. The ratio of the electric potential at point A to the electric potential at point B is:

Step-by-step solution

The electric potential V at a distance r from the center of a finite dipole of length 2a on its axial line (closer to the positive charge) is given by the exact formula: V = Kp r^2 - a^2 For point A , the distance from the center is r_A = 2a . The potential at A is: V_A = Kp (2a)^2 - a^2 = Kp 4a^2 - a^2 = Kp 3a^2 For point B , the distance from the center is r_B = 3a . The potential at B is: V_B = Kp (3a)^2 - a^2 = Kp 9a^2 - a^2 = Kp 8a^2 The ratio of the potentials is: V_A V_B = Kp 3a^2 Kp 8a^2 = 8 3 Thus, the rat