Two short magnetic dipoles m₁ and m₂ each having magnetic moment of 1 Am² are placed at point O and P respectively. The distance between OP is 1 meter. The torque experienced by the magnetic dipole m₂ due to the presence of m₁ is ........... × 10⁻⁷ Nm.

Solution

Physics sir · 4 steps

P sits on the equatorial line of m₁, so use the equatorial field and then τ = mB sin θ.

1. Locate P. m₁ points upward and the line OP is horizontal, so OP is perpendicular to m₁. That puts P on the equatorial line of m₁, at r = 1 m.

   B_(eq) = μ₀/4πm₁/r³ = 10⁻⁷ × 1/1³ = 10⁻⁷ T

2. Direction and angle. On the equatorial line the field is opposite to m₁, so at P it points straight down. m₂ points horizontally along OP, so the angle between m⃗₂ and B⃗ is 90°.
3. Torque. τ = m₂ B sin 90° = 1 × 10⁻⁷ × 1 = 1 × 10⁻⁷ N m.
4. So. The torque on m₂ is 1 × 10⁻⁷ N m, so the blank is 1.

The common slip: 2. Using the axial field μ₀/4π2m/r³ gives 2. P is on the equatorial line of m₁, so there is no factor of 2.

The idea to keep. First decide whether the point is on the axial or the equatorial line of the source dipole. Axial field has a factor 2, equatorial does not. Then use τ = mB sin θ for the angle between them.

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