The magnetic moments associated with two closely wound circular c… — Solution | JEE Physics

MCQEasyJEE 2023Magnetic Dipole & Bar Magnet

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: (Where $N_A, I_A$ and $N_B, I_B$ are number of turns and current of A and B respectively)

A
$2N_A I_A = N_B I_B$
B
$N_A = 2N_B$
C
$N_A I_A = 4N_B I_B$
D
$4N_A I_A = N_B I_B$

Answer

Correct answer:C

Step-by-step solution

Standard Method

Given: Two circular coils have equal magnetic moments. Their radii are $r_A = 10 \, cm$ and $r_B = 20 \, cm$ .

Find: The relation between $N_A I_A$ and $N_B I_B$ .

For a circular coil, magnetic moment is

M = NIA

Since $M_A = M_B$ , we get

N_A I_A A_A = N_B I_B A_B

For circular coils, $A = \pi r^2$ . Therefore,

N_A I_A \pi (0.1)^2 = N_B I_B \pi (0.2)^2

Simplifying,

N_A I_A (0.01) = N_B I_B (0.04)

N_A I_A = 4N_B I_B

Therefore, the correct option is C.

Common mistakes

Using magnetic field formula instead of magnetic moment is incorrect because the question compares magnetic moments, not fields. Use $M = NIA$ for each coil.
Forgetting that area depends on the square of radius leads to a wrong ratio. Since $A = \pi r^2$ , doubling the radius makes the area four times, not two times.
Not converting radii consistently into numerical values before squaring can cause errors. Substitute $0.1$ and $0.2$ carefully and square them before comparing.

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Answer

Step-by-step solution

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