Question

A current of 17.0 mA is maintained in a single circular loop of 2.00 \mathrm{~m} circumference. A magnetic field of 0.800T is directed parallel to the plane of the loop. (a) Calculate the magnetic moment of the loop.

Answer 1

The magnetic moment is -

M = 5.5 x $10^{-3}$ A$m^{2}$.

We have current carrying single circular loop placed in a magnetic field

parallel to the plane of the loop.

We have to determine the Magnetic moment of the loop.

What is the formula to calculate the magnetic moment of loop?

The formula to calculate the magnetic moment of the loop is -

M = NIA

where -

N -  Number of turns

I - Current in the loop

A - Area of the loop

According to the question, we have -

I = 17mA = 0.017A

Circumference (C) = 2 meters

B = 0.8 T

Now -

C = 2

2$\pi$r = 2

$\pi$r = 1

r = $\frac{1}{\pi }$

r = 0.32

Using the formula -

M = NIA

M = $\pi$NI$r^{2}$

M = 3.14 x 1 x 0.017 x 0.32 x 0.32

M = 3.14 x 4 x 0.017

M = 5.5 x $10^{-3}$ A$m^{2}$

Hence, the magnetic moment is -

M = 5.5 x $10^{-3}$ A$m^{2}$

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