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25.07.2022 - 04:06

What is the magnitude of the needle’s magnetic moment? A compass needle in a uniform magnetic field of 0.20 Tesla experiences a torque of 0.050 Newton-meter when it points in a direction 45 degrees away from the direction of the field.

Question:

What is the magnitude of the needle’s magnetic moment?

A compass needle in a uniform magnetic field of 0.20 T experiences a torque of 0.050 N-m when it points in a direction 45{eq}^{circ} {/eq} away from the direction of the field.

( Hint: {eq}A times m^2 {/eq} )

Answers (1)

Zander April 8, 2023 в 01:09

The magnetic moment of a compass needle is defined as the product of the strength of its magnetic pole and the distance between the poles. In this case, we can use the torque experienced by the needle to calculate its magnetic moment.
The formula for torque is:
? = m ? B ? sin?
where ? is the torque, m is the magnetic moment of the needle, B is the strength of the magnetic field, and ? is the angle between the direction of the needle and the direction of the magnetic field.
Using the values given in the problem, we can rearrange the formula to solve for the magnetic moment:
m = ? / (B ? sin?)
Substituting the values, we get:
m = 0.050 N-m / (0.20 T ? sin45°)
m ? 0.176 A ? m?
Therefore, the magnitude of the needle's magnetic moment is \approx imately 0.176 A ? m?.

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