Question

A current I flows in a plane rectangular current loop with height a and horizontal sides b. The loop is placed into a uniform magnetic field \(\vec{B}\) in such a way that the sides of length a are perpendicular to \(\vec{B}\), and there is an angle θ between the sides of length b and \(\vec{B}\).

Calculate τ, 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 trigonometric function [e.g., sin(θ) or cos(θ) ]. Use B for the magnitude of the magnetic field.

Answer 1

The force on the loop due to magnetic field is, \(F=I w B\)

The torque acting on the loop is, \(\tau=F b \cos \theta\)

\(=B I W b \cos \theta\)