Question:

A steel wire of length $l$ has a magnetic moment $M$. It is then bent into a semicircular arc. The new magnetic moment is

Updated On: Sep 10, 2023
  • $M$
  • $2M/\pi$
  • $M/l$
  • $M\times l$
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The Correct Option is B

Solution and Explanation

When wire is bent, length $l = \pi r$, where $r$ is the radius of the semicircular are , $\therefore$ $r = l/ \pi$ Distance between two poles of semicircular wire = $2r = 2l/pi$ Magnetic moment of semicircular wire = $m \times 2r = m \times 2l/ \pi = \frac{2}{\pi} ml$ But $ml$ is the magnetic moment of straight wire $i.e. \, ml $ = M $\therefore$ New magenetic moment of straight wire $i.e. \, ml $ = M $\therefore$ New magnetic moment = 2M/$\pi$
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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.