First slide

Magnetic dipole - Moving charges and magnetism

Question

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 $B = 7.0 μ T$

Moderate

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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