Question:
The magnetic field at the centre of a current carrying circular coil of area ' \(A\) ' is ' \(B\) '. The magnetic moment of the coil is ( \(\mu_0\) = permeability of free space)
The magnetic field at the centre of a current carrying circular coil of area ' \(A\) ' is ' \(B\) '. The magnetic moment of the coil is ( \(\mu_0\) = permeability of free space)
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Magnetic moment:
$m = IA$
Updated On: May 8, 2026
- \(\frac{2B}{\mu_0} \sqrt{\frac{A^3}{\pi}}\)
- \(\frac{\text{BA}^2}{4\mu_0\pi}\)
- \(\frac{2\pi}{\mu_0} \sqrt{A^3}\)
- \(\frac{\mu_0}{2B} \sqrt{\frac{A^3}{\pi}}\)
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The Correct Option is A
Solution and Explanation
Concept: \[ B = \frac{\mu_0 I}{2r} \quad , \quad A = \pi r^2 \]
Step 1: Find $r$. \[ r = \sqrt{\frac{A}{\pi}} \]
Step 2: Find current. \[ I = \frac{2rB}{\mu_0} \]
Step 3: Magnetic moment. \[ m = IA = \frac{2rB}{\mu_0} \cdot A \] \[ m = \frac{2B}{\mu_0} A \sqrt{\frac{A}{\pi}} = \frac{2B}{\mu_0}\sqrt{\frac{A^3}{\pi}} \] Final Answer: Option (A)
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