Question

A uniform rectangular coil of total mass \(212\;{\rm{g}}\) and dimensions \(0.5\;{\rm{m}} \times {\rm{1}}\;{\rm{m}}\) is oriented with its plane parallel to a uniform \(3\;{\rm{T}}\) magnetic field (Fig. E27.43). A current of \(2\;{\rm{A}}\) is suddenly started in the coil.

(a) About which axis (\({A_1}\) or \({A_2}\)) will the coil begin to rotate? Why?

(b) Find the initial angular acceleration of the coil just after the current is started.

Short answer

(a) The rotation axis of the coil is \({A_2}\).

Step-by-step solution

Given data

The mass of rectangular coil

\(m = 212\;{\rm{g}}\)

The length of the coil is

\(l = {\rm{1}}\;{\rm{m}}\)

The width of the coil is

\(w = 0.5\;{\rm{m}}\)

The current through the coil is

\(I = 2\;{\rm{A}}\)

The applied magnetic field is

\(B = 3\;{\rm{T}}\)

Direction of torque

The direction of torque applied by a magnetic field on a current carrying coil is the direction of the cross product of the magnetic moment of the coil and the magnetic field.

(a) Determination of the axis of rotation of the coil

The magnetic moment of the coil directed either out of the page or into the page, depending on the direction of the current. The magnetic field is directed upward. Thus, the cross product of the magnetic moment and the magnetic is directed either to the right or to the left. Hence, the rotation axis is \({A_2}\).