A uniform conducting wire of length 12a and resistance R is wound into (i) an equilateral triangle with side a and (ii) a square with side a. The magnetic dipole moments of the two coils carrying the same current I are respectively:
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Question

A uniform conducting wire of length 12a and resistance R is wound into (i) an equilateral triangle with side a and (ii) a square with side a. The magnetic dipole moments of the two coils carrying the same current I are respectively:

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G1 Physics · Accepted Answer

Step 1: The fixed wire length 12a gives 12a/(3a)=4 turns if wound into equilateral triangles of side a. Step 2: Each triangle area is (√3/4)a², so μ(triangle) = NIA = 4I(√3/4)a² = √3 Ia². Step 3: For squares of side a, one loop uses 4a wire, giving 3 turns and μ(square) = 3Ia². Step 4: Final answer: A, (√3 Ia², 3Ia²). Final answer: (A) √3 Ia² and 3Ia².