Question

Two wires of same length are bent to form the circular loop with two turns and a square loop of one turn. Both of them carry same current. The ratio of magnetic moment of circular loop of two turns to that of square loop is

• A. \(π:4\)
• B. \(4:π\)
• C. \(π:1\)
• D. \(2:π\)

Hint:

Flux density is flux over area, and permeability is B over H.

Answer 1

The Correct Option is D

Step 1: Flux density:
\(B = \frac{\Phi}{A} = \frac{3\times10^{-4}}{1.5\times10^{-4}} = 2\) T, since \(1.5\text{ cm}^2 = 1.5\times10^{-4}\text{ m}^2\).

Step 2: Permeability:
\[ \mu = \frac BH = \frac{2}{1000} = 2\times10^{-3}\text{ Wb/A-m} \]
The area conversion is the key step: using cm\(^2\) directly would give a value that is off by a factor of \(10^4\).

Final Answer:
The permeability is \(2\times10^{-3}\) Wb/A-m, option (B). \[ \boxed{2\times10^{-3}\text{ Wb/A-m}} \]