An ideal electric dipole of dipole moment p is placed at the origin, aligned along the positive x-axis. Two points, A and B, are located on the positive y-axis at distances d and 3d from the origin, respectively, as shown in the figure. If the magnitude of the electric field at point A is E₀ , what is the magnitude of the electric field at point B?

Step-by-step solution

The electric field due to an ideal (short) dipole at a point on its equatorial axis is given by: E = 1 4 ₀ p r^3 Thus, the magnitude of the electric field is inversely proportional to the cube of the distance from the dipole, E 1 r^3 . For point A at distance r = d : E_A = 1 4 ₀ p d^3 = E₀ For point B at distance r = 3d : E_B = 1 4 ₀ p (3d)^3 E_B = 1 27 ( 1 4 ₀ p d^3 ) E_B = E₀ 27 Answer: E₀ 27