Two electric dipoles of moment P and 8P are placed in opposite directions on a line at a distance of 24 cm. The electric field will be zero at the point between the dipoles whose distance from the dipole of moment P will be x₁ . When 8P is replaced by 27P keeping all other quantities the same, the distance x₁ now becomes x₂ . The difference |x₂ - x₁| is ( All the distances are measured from the centers of the dipole.

Step-by-step solution

Let the distance of the null point from the dipole of moment P be x . The distance from the second dipole is 24 - x . The electric field due to a short dipole on its axis at a distance r is given by E = 2kP r^3 . For the net electric field to be zero, the magnitudes of the electric fields due to both dipoles must be equal. Case 1: Dipoles are P and 8P 2kP x₁^3 = 2k(8P) (24 - x₁)^3 Taking the cube root on both sides: 1 x₁ = 2 24 - x₁ 24 - x₁ = 2x₁ 3x₁ = 24 x₁ = 8 cm Case 2: Dipole 8P is replaced by 27P 2kP x₂^3 = 2k