Two points A and B are located on the axial line of a short electric dipole at distances r_A and r_B from its centre, respectively. If the electrostatic potential at point A is V₀ and the potential at point B is V₀ 9 , then the ratio of their distances r_A : r_B is :

Step-by-step solution

The electrostatic potential V due to a short electric dipole at a distance r on its axial line is given by: V = 1 4 ₀ p r^2 This implies that V 1 r^2 . Therefore, the ratio of potentials at points A and B is: V_A V_B = ( r_B r_A )^2 Given that V_A = V₀ and V_B = V₀ 9 , we have: V₀ V₀ 9 = ( r_B r_A )^2 9 = ( r_B r_A )^2 Taking the square root on both sides: r_B r_A = 3 Inverting the ratio, we get: r_A r_B = 1 3 Thus, r_A : r_B = 1 : 3 . Answer: 1 : 3