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Topic: Current loop and bar magnet as magnetic dipole, field along axis and equator· Magnetic Effects of Current and Magnetism

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 side 'a'.The magnetic dipole moments of the coil in each case respectively are…

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 side 'a'.

The magnetic dipole moments of the coil in each case respectively are :

1. \(\sqrt{3}\,Ia^2\) and \(3\,Ia^2\)

2. \(3\,Ia^2\) and \(Ia^2\)

3. \(3\,Ia^2\) and \(4\,Ia^2\)

4. \(4\,Ia^2\) and \(3\,Ia^2\)

1 answer

Best answer

Answer: 1. \(\sqrt{3}\,Ia^2\) and \(3\,Ia^2\)

Key idea: magnetic moment \(M=NIA\), where N is the number of turns the wire of length 12a gives.

  • Triangle (side a, perimeter 3a): \(N=4\), area \(\dfrac{\sqrt3}4a^2\). \(M=4I\cdot\dfrac{\sqrt3}4a^2=\sqrt3Ia^2\).
  • Square (side a, perimeter 4a): \(N=3\), area \(a^2\). \(M=3Ia^2\).

Option 1.

Doubtly AI · 30 Oct 2026 AI-generated · not yet verified Report
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