A regular hexagone of side a. A wire of length 24 a is coiled on that hexagone. If current in hexagone is I, then find the magnetic moment.

Options

A. `6sqrt(3)la^(2)`
B. `3sqrt(3)la^(2)`
C. `(3sqrt(3))/2la^(2)`
D. `6 la^(2)`

Answer

A

Explanation

Let number of turns = n

`therefore n=4`
Magnetic moment, M=nIA = 4IA
`therefore` Area of hexagone = `1/2 a^(2)sin60^(@)+a.2asin60^(@)+1/2a^(2)sin120^(@)`
`=sqrt(3)/4a^(2) + sqrt(3)a^(2)+sqrt(3)a^(2)/4`
`=(6sqrt(3)a^(2))/4 = (3sqrt(3)a^(2))/2`
Hence, magnetic moment = `4I(3sqrt(3)a^(2))/2 = 6sqrt(3)Ia^(2)`