Systems of particles and rotational motion...

Question

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

(i) any equilateral triangle of side a.

(ii) a square of side a.

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

(1) 4 Ia² and 3 Ia²

(2) √3 Ia² and 3 Ia²

(3) 3 Ia² and Ia²

(4) 3 Ia² and 4 Ia²

Answer 1

Answer: (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)