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 V₀. Find the magnetic moment of the coils in each case.

Question

Philoid · Accepted Answer

Length of the wire is 12a.

Area of equilateral triangle is

Number of loops made is n=12a/3a = 4

So, magnetic moment is m=niA

Area of equilateral square is

Number of loops made is n=12a/4a = 3

So, magnetic moment is m=niA

Area of hexagon is

Number of loops made is n=12a/6a = 2

So, magnetic moment is m=niA