Torque on a Current Loop — Question 1

Question 1

The angle in the loop-torque formula is measured from the area normal

A rectangular coil has N=30 turns, sides .0500 m and .0800 m, and current I=.400 A. Its unit area normal makes 60.0 degrees with a uniform .600 T field.

1. Find the torque magnitude and its maximum possible value at the same current.

2. Express the torque using the angle between the field and the plane of the coil; evaluate that angle here.

Question 1 - Solution

The angle in the loop-torque formula is measured from the area normal

(a) Method and calculation

$$A=ab=.00400\,\mathrm{m^2},\quad\tau=N IAB\sin\theta.$$$$\tau_{\max}=NIAB=.0288\,\mathrm{N\,m},\quad\tau=.0288\sin60^\circ=.0249415\,\mathrm{N\,m}.$$

(b) Interpretation and further calculation

$$\alpha=90^\circ-\theta=30.0^\circ.$$$$\tau=NIAB\cos\alpha\quad\text{when }\alpha\text{ is the field-to-plane angle}.$$

Physical check

Confusing the plane angle with the normal angle exchanges sine and cosine and changes the predicted torque.