Question:

A current flows in a conducting wire of length L. If we bend it in a circular form, its magnetic dipole moment would be

Updated On: Jun 23, 2023
  • $\frac{IL^2}{4\pi}$
  • $\frac{IL}{4\pi}$
  • $\frac{I^2L}{4\pi}$
  • $\frac{I^2L^2}{4\pi}$
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The Correct Option is A

Solution and Explanation

Let a wire of length L is bend in a circular form of radius r
Then $ 2\pi r=L$ $\Rightarrow r=\frac{L}{2\pi} \hspace5mm ...(i)$ The magnetic dipole moment of a circular ring $ M=IA\,\, $[ A is area of the ring] or $M=I\pi r^2\hspace5mm ...(ii)$ On putting the value of r from E (i) in E (ii), we have $ M=I\pi \Bigg(\frac{L}{2\pi}\Bigg)^2 \Rightarrow M=I\pi \times\frac{L^2}{4\pi^2}$ $\Rightarrow \, \, \, M=\frac{IL^2}{4\pi}$
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Notes on Magnetism and matter

Concepts Used:

Magnetism & Matter

Magnets are used in many devices like electric bells, telephones, radio, loudspeakers, motors, fans, screwdrivers, lifting heavy iron loads, super-fast trains, especially in foreign countries, refrigerators, etc.

Magnetite is the world’s first magnet. This is also called a natural magnet.  Though magnets occur naturally, we can also impart magnetic properties to a substance. It would be an artificial magnet in that case.

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Some of the properties of the magnetic field lines are:

  • The lines and continuous and outside the magnet, the field lines originate from the North pole and terminate at the South pole
  • They form closed loops traversing inside the magnet. 
  • But here the lines seem to originate from the South pole and terminate at the North pole to form closed loops.
  • More number of close lines indicate a stronger magnetic field
  • The lines do not intersect each other
  • The tangent drawn at the field line gives the direction of the field at that point.