The magnetic field strength due to a short bar magnet at a distance r from the mid point of the magnet is B. Find the magnetic field strength at a distance 2r from the mid point of the magnet.

Concept:

Magnetic dipole:

A Magnetic Dipole consists of two unlike poles of equivalent strength and is separated by a small distance.

Magnetic moment:

It is defined as the product of pole strength and the distance between the poles of a magnet.

​⇒ M = m × 2l    

where M = magnetic moment, m = pole strength and 2l = distance between the poles

Magnetic field due to a bar magnet on the axial point:

• Magnetic field due to a bar magnet on the axial point at a distance r from the centre of magnet is given as,

If r >> l

Calculation:

Given r₁ = r, B₁ = B and r₂ = 2r

We know that magnetic field due to a bar magnet on the axial point at a distance r from the centre of magnet is given as,

     -----(1)

Similarly, magnetic field due to a bar magnet on the axial point at a distance 2r from the centre of the magnet is given as,

Hence, option 3 is correct.