The magnetic dipole moment of a circular loop carrying current I is m and the magnetic field at its centre is B₁. Keeping I constant, the dipole moment is doubled and the new central field is B₂. Find B₁/B₂.
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Question

The magnetic dipole moment of a circular loop carrying current I is m and the magnetic field at its centre is B₁. Keeping I constant, the dipole moment is doubled and the new central field is B₂. Find B₁/B₂.

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G1 Physics · Accepted Answer

For a loop, magnetic moment m=IπR² and centre field B=μ₀I/(2R). Doubling m at fixed I makes R→√2R, so B₂=B₁/√2 and B₁/B₂=√2. Hence B.