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 if sides a and iii) a regular hexagon of sides a. The coil is connected to a voltage source V0. Find the magnetic moment of the coils in each case.
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 if sides a and iii) a regular hexagon of sides a. The coil is connected to a voltage source V0. Find the magnetic moment of the coils in each case.

a) A triangle with side a that is equilateral.

Number of loops = 4

A = √3/4 a2

m = Ia2√3 is the magnetic moment.

b) In the case of a square with sides of a

A = a2

Number of loops = 3

m = 3Ia2 magnetic moment

c) For a hexagon with sides of a regular hexagon with sides of a

A = 6√3/4 a2

No.of loops = 2

Magnetic moment, m = 3√3a2I