Question

The characteristics of two coil is given below. If the magnetic moment of both coil A and B are equal then choose the correct relation,

Coil A	Coil B
Radius rA=10 cm	rB=20 cm
Number of turns NA	NB
Current IA	IB

• A. 2N_AI_A = N_BI_B
• B. N_AI_A = N_BI_B
• C. N_AI_A = 4N_BI_B
• D. N_AI_A = 2N_BI_B

Answer 1

The Correct Option is C

To solve this problem, we need to identify the relation between the parameters of two coils given that their magnetic moments are equal. The formula for the magnetic moment \( M \) of a coil is given by:

\(M = N \times I \times A\)

where:

• \(N\) is the number of turns.
• \(I\) is the current flowing through the coil.
• \(A\) is the area of the coil, calculated as \(\pi r^2\), where \(r\) is the radius of the coil.

Since both coils have equal magnetic moments, we have:

\(M_A = M_B\)

Substituting the formula for magnetic moment into this equation, we get:

\(N_A \cdot I_A \cdot \pi r_A^2 = N_B \cdot I_B \cdot \pi r_B^2\)

Since \(\pi\) is common on both sides, it can be cancelled out from the equation. Thus, we simplify to:

\(N_A \cdot I_A \cdot r_A^2 = N_B \cdot I_B \cdot r_B^2\)

Given that:

• \(r_A = 10 \text{ cm} = 0.1 \text{ m}\)
• \(r_B = 20 \text{ cm} = 0.2 \text{ m}\)

Substituting these values into the equation:

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

\(N_A \cdot I_A \cdot 0.01 = N_B \cdot I_B \cdot 0.04\)

Dividing both sides by 0.01, we get:

\(N_A \cdot I_A = 4 \cdot N_B \cdot I_B\)

Therefore, the correct relation is:

\(N_A \cdot I_A = 4 \cdot N_B \cdot I_B\)

This matches the given correct answer, confirming that Option C is indeed correct.