Magnetism at the centre of a bar magnet is ______.

CONCEPT:

• Magnetism: It is a class of physical phenomena that are mediated by magnetic fields.
  • Electric currents and the magnetic moments of elementary particles give to a rise a magnetic field, which acts on other currents and magnetic moments.
• Bar-Magnet: A bar magnet is a rectangular piece of an object, made up of iron, steel or any other ferromagnetic substance or ferromagnetic composite, that shows permanent magnetic properties.
  • It has two poles, a north and a south pole such that when suspended freely, the magnet aligns itself so that the northern pole points towards the magnetic north pole of the earth.
• Uses of Bar Magnet. Bar magnets are used as stirrers in the laboratory for magnetic experiments.
  • Electronic devices such as telephones, radios, and television sets use magnets.

CALCULATION:

• If we consider a bar magnet of length l, then the magnetic moment is M = 2m × I

Where m is the magnitude of poles.

• Considering the distance r from the center of the bar magnet, we can write magnetic field intensity as a product of magnetic field strength and positional feature.

Therefore, the field intensity at a distance r is given by (r2 - l2)2.

• The magnetic field of a bar magnet at an axial point is given by

\(\Rightarrow B = \frac{{{\mu _o}}}{{4\pi }}\frac{{2Mr}}{{{{\left( {{r^2} - {l^2}} \right)}^2}}}\)

At the center of the magnet, r = 0, so 

\(\Rightarrow B = \frac{{{\mu _o}}}{{4\pi }}\frac{{2Mr}}{{{{\left( {{r^2} - {l^2}} \right)}^2}}} = \frac{{{\mu _o}}}{{4\pi }}\frac{{2M \times 0}}{{{{\left( {{r^2} - {l^2}} \right)}^2}}} = 0 \)

• Hence option 4 is correct.