Question

A straight wire currying current I is turned into a circular Loop. If the magnitude of magnetic moment associated with it in MKs unit is M, the length of wire will be 

(a) 4πMI 

(b) √[(4πM)/I] 

(c) √[(4πI)/M] 

(d) [(Mπ)/(4I)]

Answer 1

The correct option (b) √[(4πM)/I]   

Explanation:

Magnetic moments of current loop,

M = I × area

= I × πR²   (1)

Length of wire be L.

L is converted to circular loop of radius R

∴  L = 2πR

R = (L/2π)

From (1)

M = I × π(L/2π)² = (IL²/4π)

L² = [(4πM)/I]

L = √[(4πM)/I]