The magnetic moment of a thin round loop with current in the loop of the radius $$R=100$$ mm is x×$$10$$−$$2$$ $$Am2$$, and the magnetic induction at its center is equal to $$B=7.0$$μT

$$Bcenter=$$μ$$0i2R$$ ⇒$$i=2RB$$μ$$0$$∴Magnetic Moment $$M=iA$$⇒$$M=i$$.π$$R2$$ ⇒$$M=2RB$$μ$$0$$$$π$$$$R2=2$$×$$0.1$$×$$7.0$$×$$10-6$$×π×$$0.1$$×$$0.14$$π×$$10-7=0003.50$$×$$10$$−$$2Am2$$

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The magnetic moment of a thin round loop with current in the loop of the radius $R = 100 m m$ is $x \times 10^{- 2} A m^{2}$ , and the magnetic induction at its center is equal to $B = 7.0 μ T$

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Solution

$B_{center} = \frac{μ_{0} i}{2 R} \Rightarrow i = \frac{2 R B}{μ_{0}}$
$∴ M a g n e t i c M o m e n t M = i A$
$\Rightarrow M = i . π R^{2} \Rightarrow M = (\frac{2 R B}{μ_{0}}) π R^{2} = \frac{2 \times 0.1 \times 7.0 \times 10^{- 6} \times π \times 0.1 \times 0.1}{4 π \times 10^{- 7}} = 0003.50 \times 10^{- 2} A m^{2}$

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Magnetic dipole - Moving charges and magnetism

Remember concepts with our Masterclasses.

The magnetic moment of a thin round loop with current in the loop of the radius R=100 mm is x×10−2 Am2, and the magnetic induction at its center is equal to B=7.0μT

Bcenter=μ0i2R ⇒i=2RBμ0∴Magnetic Moment M=iA⇒M=i.πR2 ⇒M=2RBμ0πR2=2×0.1×7.0×10-6×π×0.1×0.14π×10-7=0003.50×10−2Am2

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The magnetic moment of a thin round loop with current in the loop of the radius $R = 100 m m$ is $x \times 10^{- 2} A m^{2}$ , and the magnetic induction at its center is equal to $B = 7.0 μ T$