The magnetic moments associated with two clos | vedclass

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(C) The magnetic moment $m$ of a current-carrying coil is given by $m = N I A$,where $N$ is the number of turns,$I$ is the current,and $A$ is the area

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$N_A I_A = 4 \ N_B I_B$

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(C) The magnetic moment $m$ of a current-carrying coil is given by $m = N I A$,where $N$ is the number of turns,$I$ is the current,and $A$ is the area of the coil.Given that the magnetic moments of coils $A$ and $B$ are equal,$m_A = m_B$.Therefore,$N_A I_A A_A = N_B I_B A_B$.Since the coils are circular,the area $A = \pi r^2$. Thus,$N_A I_A (\pi r_A^2) = N_B I_B (\pi r_B^2)$.Substituting the given radii $r_A = 10 \ cm$ and $r_B = 20 \ cm$:$N_A I_A (10)^2 = N_B I_B (20)^2$.$N_A I_A (100) = N_B I_B (400)$.$N_A I_A = 4 \ N_B I_B$.

The magnetic moments associated with two closely wound circular coils $A$ and $B$ of radius $r_A = 10 \ cm$ and $r_B = 20 \ cm$ respectively are equal. If $N_A, I_A$ and $N_B, I_B$ are the number of turns and current of $A$ and $B$ respectively,then which of the following relations is correct?

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