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

Option: 1

4 \mathrm{~N}_{\mathrm{A}} \mathrm{I}_{\mathrm{A}}=\mathrm{N}_{\mathrm{B}} \mathrm{I}_{\mathrm{B}}


Option: 2

\mathrm{N}_{\mathrm{A}}=2 \mathrm{~N}_{\mathrm{B}}


Option: 3

\mathrm{N}_{\mathrm{A}} \mathrm{I}_{\mathrm{A}}=4 \mathrm{~N}_{\mathrm{B}} \mathrm{I}_{\mathrm{B}}


Option: 4

2 \mathrm{~N}_{\mathrm{A}} \mathrm{I}_{\mathrm{A}}=\mathrm{N}_{\mathrm{B}} \mathrm{I}_{\mathrm{B}}


Answers (1)

best_answer

Magnetic moment m = IAN

Magnetic moment of coil A\rightarrow

\begin{aligned} & \mathrm{m}_{\Lambda}=\mathrm{I}_{\mathrm{A}} \pi \mathrm{r}_{\Lambda}^2 \mathrm{~N}_{\Lambda} \\ & \mathrm{m}_{\mathrm{A}}=\mathrm{I}_{\mathrm{A}} \pi \mathrm{N}_{\mathrm{A}}(10)^2 \end{aligned} ___________(1)

Magnetic moment of coil B\rightarrow

\begin{array}{ll} & \mathrm{m}_{\mathrm{B}}=\mathrm{I}_{\mathrm{B}} \mathrm{N}_{\mathrm{B}} \pi \mathrm{r}_{\mathrm{B}}^2 \\ \text { Now } & \mathrm{m}_{\mathrm{B}}=\mathrm{I}_{\mathrm{B}} \mathrm{N}_{\mathrm{B}} \pi(20)^2 \\ & \mathrm{~m}_{\mathrm{A}}=\mathrm{m}_{\mathrm{B}} \\ & \mathrm{I}_{\mathrm{A}} \cdot \pi \mathrm{N}_{\mathrm{A}}(100)=\mathrm{I}_{\mathrm{B}} \mathrm{N}_{\mathrm{B}} \pi 400 \\ & \mathrm{I}_{\mathrm{A}} \mathrm{N}_{\mathrm{A}}=4 \mathrm{I}_{\mathrm{B}} \mathrm{N}_{\mathrm{B}} \end{array}________(2)

 

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