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### College Physics (Urone)

Book edition 1st Edition
Author(s) Paul Peter Urone
Pages 1272 pages
ISBN 9781938168000

# A 200-turn circular loop of radius ${\mathbf{50}}{\mathbf{.}}{\mathbf{0}}{\mathbf{}}{\mathbf{cm}}$ 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 ${\mathbf{3}}{\mathbf{.}}{\mathbf{00}}{\mathbf{×}}{{\mathbf{10}}}^{\mathbf{‐}\mathbf{5}}{\mathbf{}}{\mathbf{T}}$ . What are the direction and magnitude of the torque on the loop? (b) Does this device have any practical applications as a motor?

(a) Torque on the loop is $0.47\mathrm{N}‐\mathrm{m}$.

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

See the step by step solution

## Step 1:  Definition of torque

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

## Step2: To get the torque

First,

We will get the area of the circular loop then we will use the equation

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

As the loop is vertical and the magnetic field is pointing to the north, the angle $\mathrm{\theta }=90°$ that leads to the value of $\mathrm{sin}\left(90°\right)=1$.

Therefore using equation (1), we can write the maximum value of torque such that,

${\mathrm{\tau }}_{\mathrm{max}}=\mathrm{NIAB}$……………………..(2)

## Step 3: Finding the direction of the torque (a)

The area of the loop can be estimated as,

$\mathrm{A}={\mathrm{\pi r}}^{2}\phantom{\rule{0ex}{0ex}}=\mathrm{\pi }×{\left(0.50\mathrm{m}\right)}^{2}\phantom{\rule{0ex}{0ex}}=0.79{\mathrm{m}}^{2}$

Then using equation (2), we will determine the torque such that,

${\mathrm{\tau }}_{\mathrm{max}}=200×100\mathrm{A}×0.79{\mathrm{m}}^{2}3.00×{10}^{‐5}\mathrm{T}\phantom{\rule{0ex}{0ex}}=0.47\mathrm{N}‐\mathrm{m}$

As the current in the loop circulates clockwise and the field points to the north, the torque's direction will be clockwise as well.

## Step 4: Does this device have any practical applications as a motor?(b)

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