Question

A wire of length 2m carries a current of 3.14 ampere is bend to firm a circle. the magnetic moment of the coil is

Answer 1

length of wire = 2m
as this wire is bent in form of circle
2πr = length of wire = 2 m
r = 1/π
current = i = 3.14 ≈ π Amperes
magnetic moment of coil is
$m = (i)(area)$
m = (π) [π (1/π)^2 ]
m = π/π
m = 1 amp-metre.square

Answer 2

Given:

• Length of wire = 2 metres
• Current = 3.14 amperes

To find:

• Magnetic moment of loop ?

Calculation:

First of all, leta calculate the radius of the loop:

$2\pi r = l$

$\implies \: r = \dfrac{l}{2\pi}$

$\implies \: r = \dfrac{2}{2\pi}$

$\implies \: r = \dfrac{1}{\pi} \: metres$

Now, let's find out the magnetic moment :

• Let Magnetic Moment be M :

$M = i \times area$

$\implies \: M = 3.14 \times (\pi {r}^{2} )$

$\implies \: M = 3.14 \times \pi \times \dfrac{1}{ {\pi}^{2} }$

• Putting π = 3.14 :

$\implies \: M = \dfrac{ {\pi}^{2} }{ {\pi}^{2} }$

$\implies \: M = 1 \: ampere \: {m}^{2}$

So, magnetic moment is 1 Am².