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A current of 30.0 mA is maintained in a single circular loop of 3.80 m circumference. A magnetic field of 0.510 T is directed parallel to the plane of the loop.(a) Calculate the magnetic moment of the loop.

Question

A current of 30.0 mA is maintained in a single circular loop of 3.80 m circumference. A magnetic field of 0.510 T is directed parallel to the plane of the loop.(a) Calculate the magnetic moment of the loop.

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Solution

The magnetic moment (μ) of a current loop is given by the product of the current (I) and the area (A) of the loop. The formula is:

μ = I * A

Given that the current (I) is 30.0 mA or 0.030 A and the circumference of the loop is 3.80 m, we can find the radius (r) of the loop using the formula for the circumference of a circle:

C = 2πr r = C / (2π)

Substituting the given circumference:

r = 3.80 m / (2π) = 0.604 m

The area (A) of a circle is given by the formula:

A = πr²

Substituting the calculated radius:

A = π * (0.604 m)² = 1.15 m²

Now we can calculate the magnetic moment:

μ = I * A = 0.030 A * 1.15 m² = 0.0345 A.m²

So, the magnetic moment of the loop is 0.0345 A.m².

This problem has been solved

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