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# The magnetic moment associated with a circular coil of $35$ turns and radius $25\,cm$, if it carries a current of $11\,A$ is?

Last updated date: 18th Mar 2023
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Hint: In order to answer this problem let us first get some idea about coil. An electromagnetic coil is an electrical conductor in the form of a coil, spiral, or helix, such as a wire. Or we can say that a coil is a length of something wound in a concentric ring pattern.

Let's get some idea about magnetic moments. The magnetic moment is the magnetic power and orientation of a magnet or other magnetic field-producing object. Loops of electric current (such as electromagnets), permanent magnets, and elementary particles such as electrons, various molecules, and several astronomical phenomena are examples of objects with magnetic moments such as many planets, some moons, stars, etc.

Instead of directly going to the magnetic moment associated with a circular coil let us first get some idea about the magnetic moment of a current carrying wire. The magnetic moment of a current carrying wire is given by $M = IA$. Now the magnetic moment associated with this circular coil is:
$M = NIA$
Here, $M =$Magnetic moment, $A =$Area enclosed. $= \pi {r^2}$ and $N =$ Number of turns.
Given :
$N = 35$
$\Rightarrow r = 25\,cm = 25 \times {10^{ - 2}}$
$\Rightarrow I = 11A$
Magnetic moment associated with the circular coil is:
$M = NIA \\ \Rightarrow M = NI\pi {r^2} \\ \Rightarrow M = 35 \times 11 \times 3.14 \times {(25 \times {10^{ - 2}})^2} \\ \therefore M = 75.56\,A{m^2} \\$

Hence, the magnetic moment associated with a circular coil is $75.56\,A{m^2}$.

Note:A magnet's magnetic moment is a quantity that defines the force that it will exert on electric currents as well as the torque that a magnetic field can exert on it. Magnetic moments can be found in a loop of electric current, a bar magnet, an electron, a molecule, or a world.