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 - Physics MCQ NEET 2021 2026 | ExamTest.live

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A uniform conducting wire of length 12 a and resistance R is wound up as a current carrying coil in the shape of (i) an equilateral triangle of side a, and (ii) a square of side a . The magnetic dipole moments of the coil in each case respectively are:

Solution & Step-by-step Explanation

Total length L = 12 a .Case (i): Equilateral triangle of side a .Perimeter of one turn = 3 a .Number of turns n_{1} = \frac{12 a}{3 a} = 4 .Area of triangle A_{1} = \frac{3}{4} a^{2} .Magnetic moment M_{1} = n_{1} I A_{1} = 4 \times I \times \frac{3}{4} a^{2} = 3 I a^{2} .Case (ii): Square of side a .Perimeter of one turn = 4 a .Number of turns n_{2} = \frac{12 a}{4 a} = 3 .Area of square A_{2} = a^{2} .Magnetic moment M_{2} = n_{2} I A_{2} = 3 \times I \times a^{2} = 3 I a^{2} .

Try it yourself before checking the explanation above.

A uniform conducting wire of length 12 a and resistance R is wound up as a current carrying coil in the shape of (i) an equilateral triangle of side a, and (ii) a square of side a . The magnetic dipole moments of the coil in each case respectively are:

3 I a^{2} and 4 I a^{2}

4 I a^{2} and 3 I a^{2}

3 I a^{2} and 3 I a^{2}

3 I a^{2} and I a^{2}

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