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 sides a and, (iii) a regular hexagon of sides a. The coil is connected to a voltage source `V_0`. Find the magnetic moment of the coils in each case.

Answer 1

(i) No. of turns, `n=4`
Area of triangle `A=1/2axxasin60^@=a^2sqrt3//4`
(ii) `n=3`, area `A=axxa=a^2`
(iii) `n=2`, area `A=6[a/2xxa/2tan60^@]=(3sqrt3)/(2)a^2`
Magnetic moment, `M=nIA`
For (i), `M_1=4xxIxxa^2sqrt3//4` `=sqrt3a^2I` For (ii), `M_2=3xxIxxa^2=3a^2I`
For (iii), `M_3=2xxIxx(3sqrt3)/(2)a^2` `=3sqrt3a^2I`