Question:

A bar magnet of length '$l$' and magnetic dipole moment 'M' is bent in the form of an arc as shown in figure. The new magnetic dipole moment will be

Updated On: Apr 29, 2024
  • $ \frac{M}{2}$
  • $M$
  • $ \frac{3}{\pi} M$
  • $ \frac{2}{\pi} M$
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The Correct Option is C

Solution and Explanation

Let magnetic pole strength be m then
M$ = m \ell$

In new situation
$M' = (m) \left(2r \,\,sin \frac{60^\circ}{2}\right) where\, \, r \left( \frac{\pi}{3}\right) = \ell$
$M' = 2m \left(\frac {2 \ell}{\pi}\right) \left(\frac{1}{2}\right) = \frac{3m\ell}{\pi} = \frac {3M}{\pi}$
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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.