22.8 Torque on a Current Loop: Motors and Meters

(a) By how many percent is the torque of a motor decreased if its permanent magnets lose 5.0% of their strength? (b) How many percent would the current need to be increased to return the torque to original values?

Find the current through a loop needed to create a maximum torque of $9 . \text{00 N} \cdot \text{m}.$ The loop has 50 square turns that are 15.0 cm on a side and is in a uniform 0.800-T magnetic field.

Since the equation for torque on a current-carrying loop is $\tau = \text{NIAB} \text{sin} \theta$, the units of $N \cdot m$ must equal units of $A \cdot m^{2} T$. Verify this.

A proton has a magnetic field due to its spin on its axis. The field is similar to that created by a circular current loop $0 . \text{650} \times \text{10}^{- \text{15}} m$ in radius with a current of $1 . \text{05} \times \text{10}^{4} A$ (no kidding). Find the maximum torque on a proton in a 2.50-T field. (This is a significant torque on a small particle.)

Repeat the exercise, but with the loop lying flat on the ground with its current circulating counterclockwise (when viewed from above) in a location where the Earth’s field is north, but at an angle $\text{45} . 0º$ below the horizontal and with a strength of $\text{6}. \text{00} \times \text{10}^{- 5} T$.