Physics · Moving Charges And Magnetism · NEET
In tau = NIAB sin(theta), theta is measured from the NORMAL (area vector m) to B, not from the plane. So when the loop's plane is PARALLEL to B, the normal is perpendicular to B, theta = 90, and torque is MAXIMUM (tau = NIAB). When the plane is perpendicular to B, the normal is along B, theta = 0, and torque is ZERO. This is the single most common mix-up in NEET. Quick check: max torque when the field lies IN the plane of the loop.
In a uniform B, the two opposite sides of the loop carry current in opposite directions, so they feel equal and opposite forces (F = IL x B). Equal + opposite forces means net force = 0, so the loop does not move as a whole. But these two forces act along different lines (a separation d apart), forming a couple. A couple produces a turning effect (torque) even though it gives no net force. That is why the loop rotates but does not translate.
Torque tau = NIAB sin(theta). Maximum when theta = 90 (loop plane contains B / normal perpendicular to B): tau_max = NIAB. Zero when theta = 0 or 180 (normal parallel or anti-parallel to B). theta = 0 is STABLE equilibrium (loop face square-on to B); theta = 180 is UNSTABLE. So the loop naturally rotates to align its magnetic moment m along B.
They are the same law written two ways. tau = m x B is the vector form, where m = NIA is the magnetic dipole moment vector (direction by right-hand curl rule, along the normal). Its magnitude gives tau = mB sin(theta) = (NIA)B sin(theta) = NIAB sin(theta), the scalar form. Use the scalar form for magnitude in numericals; use the vector form when you need the direction of the turning axis.
Yes. Each turn contributes its own torque, so an N-turn coil has magnetic moment m = NIA and torque tau = NIAB sin(theta). Doubling the turns doubles both the moment and the torque (for the same current, area and field). This is exactly why galvanometer coils are wound with many turns: more turns give more torque for a tiny current.
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.
tau = NIAB sin(theta) in scalar form, or tau = m x B in vector form, where m = NIA is the magnetic dipole moment, N is turns, I is current, A is loop area, B is the field, and theta is the angle between the normal and B.
A current loop has a magnetic moment m = NIA and, in a field, it experiences a torque tau = m x B that tries to align m with B - exactly like a bar magnet or an electric dipole. So the loop is the magnetic equivalent of a dipole.
No. In a UNIFORM field the forces on opposite sides cancel, giving zero net force but a non-zero torque (a couple). A net force appears only in a NON-uniform field.
Ampere metre squared (A m^2). Since m = NIA, the unit is (ampere)(metre^2). Torque then has units of A m^2 x T = N m (newton metre).
The deflecting torque tau = NIAB turns the coil; a spring provides a restoring torque proportional to the angle. At balance NIAB = k(phi), so deflection phi is proportional to current I - the basis of current measurement.
