Two ideal electric dipoles A and B, having their dipole moment p₁ and p₂ respectively are placed on a plane with their centres at O as shown in the figure. At point C on the axis of dipole A, the resultant electric field is making an angle of 37° with the axis. The ratio of the dipole moment of A and B, p₁/p₂ is : (take sin 37° = 3/5)

Solution

Physics sir · 4 steps

C is on A's axis but on B's equatorial line, so the axial field is twice as strong per unit dipole moment.

1. Field from A. C lies on the axis of A at distance r from O. The axial field of a dipole is E_A = 2kp₁/r³, directed along p₁, that is, along the axis towards C.
2. Field from B. B is perpendicular to OC, so C lies on its equatorial line. Here E_B = kp₂/r³, directed opposite to p₂, which makes it perpendicular to the axis of A.
3. Use the angle. The two fields are at right angles, so the angle θ the resultant makes with A's axis satisfies tan θ = E_B/E_A. With sin 37° = 3/5, cos 37° = 4/5 and tan 37° = 3/4.

   tan 37° = E_B/E_A = (kp₂/r³)/(2kp₁/r³) = p₂/2p₁ = 3/4

4. So. p₂ = 3/2p₁, which gives p₁/p₂ = 2/3. The answer is option (c).

The idea to keep. At the same distance, a dipole's axial field is 2kp/r³ and its equatorial field is kp/r³. First decide which line the point lies on for each dipole, then add the fields as vectors.

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