The magnetic moments associated with two closely wound circular coils A and B of radius r _ A = 10cmand r _ B = 20cm respectively are equal if: (Where N _ A , I _ A and N _ B , I _ B are number of turn and current of

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Correct answer: C. N _ A I _ A = 4 N _ B I _ B

As magnetic moment of both the coil is the same,

${\mu}_{1} = {\mu}_{2}$

$⇒ {N}_{A}\left[{I}_{A}\pi\left({r}_{A}^{2}\right)\right] = {N}_{B}\left[{I}_{B}\pi{\left({r}_{B}^{2}\right)}^{2}\right] ⇒ {N}_{A}\left[{I}_{A}{\left(0 . 10\right)}^{2}\right] = {N}_{B}\left[{I}_{B}{\left(0 . 20\right)}^{2}\right] ⇒ {I}_{A}{N}_{A} = 4{I}_{B}{N}_{B}$

The magnetic moments associated with two closely wound circular...

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