Physics · Moving Charges And Magnetism · NEET
The work you do against the magnetic torque is W = MB(cos θ1 - cos θ2). Here θ1 is the START angle and θ2 is the FINAL angle, both measured between the magnetic moment M and the field B. It is start-cosine minus final-cosine. Example: 0 to 180 degrees gives W = MB(cos0 - cos180) = MB(1 - (-1)) = 2MB, a positive value, which makes sense because you must push the loop away from its stable aligned position.
At 0 degrees M is along B (stable, lowest energy U = -MB). At 180 degrees M is opposite to B (unstable, highest energy U = +MB). The work you do equals the change in potential energy: W = U_final - U_initial = (+MB) - (-MB) = 2MB. The factor of 2 appears because you climb from the lowest energy point all the way to the highest energy point.
Always from the NORMAL to the loop, because the magnetic moment vector M points along the normal (by the right-hand rule), not along the plane. So θ is the angle between M and B. A very common trap: a loop lying flat 'in' the field with its plane parallel to B actually has M perpendicular to B, so θ = 90 degrees, not 0 degrees. Read the geometry carefully.
For a slow (quasi-static) rotation they are numerically equal: W_external = ΔU = MB(cos θ1 - cos θ2). The magnetic field itself does the opposite work, W_magnetic = -ΔU. So when a problem says 'work done against the torque' or 'work done by external agent', use W = MB(cos θ1 - cos θ2). The potential energy at any single angle is U(θ) = -MB cos θ = -M·B.
A 250-turn rectangular coil of length 2.1 cm and width 1.25 cm carries a current of 85 A and is subjected to a magnetic field of strength 0.85 T. The work done for rotating the coil by 180 degrees against the torque is:
Try the real previous-year questions from this chapter — each with the answer and a full solution.
W = MB(cos θ1 - cos θ2), where M = NIA is the magnetic moment, B is the field, and θ1, θ2 are the initial and final angles between M and B.
W = 2MB = 2NIAB. It flips the moment from fully aligned (stable) to fully anti-aligned (unstable), so it is the maximum possible work.
U = -M·B = -MB cos θ. It is minimum (-MB) when M is along B and maximum (+MB) when M is opposite to B.
When the loop turns toward alignment (θ decreasing toward 0), the field does positive work and potential energy decreases. To turn it away from alignment, an external agent must do positive work.
Yes. Use M = NIA. For a coil with N turns, every formula scales with N, so forgetting N is the most common NEET mistake in these numericals.
