A uniform conducting wire of length 12a and resistance 'R' is wound up as a current carrying coil in the shape of
1. an equilateral triangle of side 'a'
2. a square of side 'a'
The magnetic dipole moments of the coil in each case resp. are.

Options

A. `3 la^(2) and la^(2)`
B. `3l a^(2) and 4l a^(2)`
C. `4 la^(2) and 3la^(2)`
D. `sqrt3l a^(2) and 3 l a^(2)`

Answer

D

Explanation

For triangle of side a `n= (12a)/(3a)`
n = 4 number of turns The magnetic moment of the coils `M= nIA = 4I ((sqrt3)/(4) a^(2)) = sqrt3 Ia^(2)`
For square of side a `n= (12a)/(4a)= 3`
The magnetic moment of the coils `M= nIA= 3(I) a^(2)`