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 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.
Solution:
(a) An equilateral triangle with side a
No.of loops = 4
Area of the triangle A = √3/4 a2
Magnetic moment, m = Ia2√3
(b) For a square with sides a
Area, A = a2
No.of loops = 3
Magnetic moment, m = 3Ia2
(c) For a regular hexagon with sides a
Area, A = 6√3/4 a2
No.of loops = 2
Magnetic moment, m = 3√3a2I
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