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Q48PE

Expert-verifiedFound in: Page 813

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 ${\mathbf{3}}{\mathbf{.}}{\mathbf{00}}{\mathbf{\times}}{{\mathbf{10}}}^{\mathbf{\u2010}\mathbf{5}}{\mathbf{}}{\mathbf{T}}$ . 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 $0.47\mathrm{N}\u2010\mathrm{m}$.

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

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

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 $\mathrm{\theta}=90\xb0$ that leads to the value of $\mathrm{sin}\left(90\xb0\right)=1$.

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

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

The area of the loop can be estimated as,

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

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

${\mathrm{\tau}}_{\mathrm{max}}=200\times 100\mathrm{A}\times 0.79{\mathrm{m}}^{2}3.00\times {10}^{\u20105}\mathrm{T}\phantom{\rule{0ex}{0ex}}=0.47\mathrm{N}\u2010\mathrm{m}$

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

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

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