The electric field at point p due to an electric dipole is E. The electric field at point R on equitorial line will be E/x. The value of x :

Solution

Physics sir · 4 steps

Axial field has a 2 in front, equatorial does not, and R is twice as far: multiply the two effects.

1. Read the distances. From the figure, P is on the axis at distance r from the centre O. R is on the equatorial line at distance 2r from O. Treat the dipole as short compared with these distances, so the standard dipole formulas apply.

   Eₐₓᵢₐₗ = 2kp/d³, E_(equatorial) = kp/d³

2. Field at P. With d = r, the axial field is E = 2kp/r³.
3. Field at R. With d = 2r, the equatorial field is kp/(2r)³ = kp/8r³. Divide by E: (kp/8r³)/(2kp/r³) = 1/16.
4. So. The field at R is E/16, so x = 16.

The common slip: 8. Dropping the factor 2 in the axial formula, as if axial and equatorial fields were equal at the same distance, gives 8, not 16.

The idea to keep. At the same distance, the axial field of a dipole is twice the equatorial field. Both fall as 1/d³, so doubling the distance cuts the field by a factor of 8.

Answer from the NTA final answer key. Solution by PrepWiser.