Question

A uniform conducting wire of length 12a and resistance 'R' is wound up as a current carrying coil in the shape of,

(i) an equilateral triangle of side 'a'. 

(ii) a square of side 'a'. 

The magnetic dipole moments of the coil in each case respectively are : 

(1) √3Ia² and 3Ia² 

(2) 3 Ia² and Ia² 

(3) 3 Ia² and Ia² 

(4) 4 Ia² and 3 Ia²

Answer 1

Option : (1). √3Ia² and 3Ia²

M₁ = (\(\frac{\sqrt{3}}{4}a^2\))I x 4 = √3Ia² 

(no. of turns = 4)

M₂ = a²I × 3 = 3Ia² 

(no. of turns = 3)