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Torque on a Current - Carrying Loop
Consider torque τ that acts on a loop with current I in a uniform magnetic field B. Magnetic forces act on every element of the loop. Net torque equals
τ = ISBsinα = μBsinα,
Here, S is the area of the loop, and α is the angle between the normal to the plane of the loop and the direction of the magnetic field B. The product μ = ISn, where n is the unit vector normal to the plane, is called the magnetic moment of the loop. The direction of the magnetic moment μ is in synch with the direction of the current in the loop, in accordance with the right-hand rule.
The torque τ tends to turn the loop in such a way that the direction of the magnetic moment μ coincides with the direction of the magnetic field B. When they coincide, the loop is in stable equilibrium position (τ = 0) . If μ and B are anti-parallel, the equilibrium is unstable.
The torque can be found with greatest ease in case of a rectangular current loop, assuming that B = Bx, and that the axis of the turn coincides with the z-axis. In this case, the torque is the result of two forces parallel to the axes of the turn and acting on the loop's sides.
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