Magnetic Effects & Magnetism

JEE Main level, single correct, medium

246 of 276

Question 246 of 276

The magnetic moments associated with two closely wound circular coils AA and BB of radius rA=10cmandrB=20cm{r}_{A}=10cm\text{and}{r}_{B}=20cm respectively are equal if: (Where NA,IAandNB,IB{N}_{A},{I}_{A}\text{and}{N}_{B},{I}_{B} are number of turn and current of AandBA\text{and}B respectively)

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Answer: (C) NAIA=4NBIB{N}_{A}{I}_{A}=4{N}_{B}{I}_{B}

As magnetic moment of both the coil is the same,
μ1=μ2{\mu }_{1}={\mu }_{2}
⇒NA[IAπ(rA2)]=NB[IBπ(rB2)2]⇒NA[IA(0.10)2]=NB[IB(0.20)2]⇒IANA=4IBNB\Rightarrow {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] \Rightarrow {N}_{A}\left[{I}_{A}{\left(0.10\right)}^{2}\right]={N}_{B}\left[{I}_{B}{\left(0.20\right)}^{2}\right] \Rightarrow {I}_{A}{N}_{A}=4{I}_{B}{N}_{B}

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