Learning Goal: To understand the origin of the torque on a current loop due to t

Question

Learning Goal: To understand the origin of the torque on a current loop due to the magnetic forces on the current-carrying wires. Part A This problem will show you how to calculate the torque on a magnetic dipole in a uniform magnetic field. We start with a rectangular current loop, the shape of which alows us to calculate the Lorentz forces explicitly. Then we generalize our result. Even if you already know the general formula to solve this problem, you might find it instructive to discover where it comes from. A current I flows in a plane rectangular current loop with height w and horizontal sides b. The loop is placed into a uniform magnetic field B in such a way that the sides of length to are perpendicular to B (Figure 1), and there is an angle between the sides of length b and B (Figure 2). Calculate T, the magnitude of the torque about the vertical axis of the current loop due to the interaction of the current through the loop with the magnetic field. Express the magnitude of the torque in terms of the given variables. You will need a trigonomeric function [e.g., sin(6) or cos(0)1. Use B for the magnitude of the magnetic field. Figure

Explanation / Answer

the torque acting on the rectangular current loop,

Torque=magnitude of force*lever arm

Torque=(I*W*B)*(b*sin(theta))

=I*(b*w)*B*sin(theta)

or

=I*A*B*sin(theta)

here, theta is angle between the B and normal of the area

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