Question

Repeat Exercise 22.41 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 $\mathbf{45}\mathbf{°}$below the horizontal and with a strength of$\mathbf{6}\mathbf{.}\mathbf{00}\mathbf{\times }{\mathbf{10}}^{\mathbf{‐}\mathbf{5}}\mathbf{}\mathbf{T}$.

Short answer

(a) Maximum torque on a loop is$0.67\mathrm{N}‐\mathrm{m}$and direction is west.

(b) The torque is very small so the loop will not have any practical application as a motor.

Step-by-step solution

Definition of torque

Torque, also known as force moment, is the tendency of a force to spin the body to which it is applied in physics.

We can use the equation to determine the torque,

$\mathbf{\tau }\mathbf{=}\mathbf{NIABsin}\left(\theta \right)$ ………….(1)

Finding the torque using the formula(a)

Substitute the values in the equation (1), and we get

$$\begin{gathered} \mathrm{\tau }=200\times 100\mathrm{A}\times 0.79{\mathrm{m}}^2\left(6.00\times {10}^{‐5}\mathrm{T}\right)\times \sin \left(45°\right) \\ =0.67\mathrm{N}‐\mathrm{m} \end{gathered}$$

Hence, the required maximum torque on a loop is $0.67\mathrm{N}‐\mathrm{m}$

Considering direction of force and current we find that the direction of torque is in west.

Justification (b)

The torque is very small so the loop will not have any practical application as a motor.