22.8 Torque on a current loop: motors and meters  (Page 2/4)

Draw a diagram and use RHR-1 to show that the forces on the top and bottom segments of the motor’s current loop in [link] are vertical and produce no torque about the axis of rotation.

(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?

(a) What is the maximum torque on a 150-turn square loop of wire 18.0 cm on a side that carries a 50.0-A current in a 1.60-T field? (b) What is the torque when $\theta$ is $\text{10}\text{.}\mathrm{9º?}$

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

Calculate the magnetic field strength needed on a 200-turn square loop 20.0 cm on a side to create a maximum torque of $\text{300 N}\cdot \text{m}$ if the loop is carrying 25.0 A.

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

(a) At what angle $\theta$ is the torque on a current loop 90.0% of maximum? (b) 50.0% of maximum? (c) 10.0% of maximum?

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 $0\text{.}\text{650}\times {\text{10}}^{-\text{15}}\mathrm{m}$ in radius with a current of $1\text{.}\text{05}\times {\text{10}}^4\mathrm{A}$ (no kidding). Find the maximum torque on a proton in a 2.50-T field. (This is a significant torque on a small particle.)

(a) A 200-turn circular loop of radius 50.0 cm is vertical, with its axis on an east-west line. A current of 100 A circulates clockwise in the loop when viewed from the east. The Earth’s field here is due north, parallel to the ground, with a strength of $3\text{.}\text{00}\times {\text{10}}^{-5}\mathrm{T}$ . What are the direction and magnitude of the torque on the loop? (b) Does this device have any practical applications as a motor?

Repeat [link] , 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 $\text{45}\text{.}\mathrm{0º}$ below the horizontal and with a strength of $\text{6.}\text{00}\times {\text{10}}^{-5}\mathrm{T}$ .