When we trace magnetic lines of force around a magnet using a compass needle, what we obtain is the resultant of the magnetic field of magnet and that of the earth. As earth’s field is fixed the resultant field would depend on the direction in which the magnet is placed in the plot of the resultant field would depend on the direction in resultant field we come across points at which field (B) due to the magnet becomes equal and opposite to the horizontal component (H) of earth’s field points will be zero. These points where net magnetic field due to the magnet and magnetic field of the earth is zero are called neutral points. A small compass needle paved at a neutral point shall experience no force/torque. Therefore, it can set itself in any direction, which may be different which may be different from the usual N – S direction.
We shall trace the lines of force in the following two cases.
Magnet placed with its N-pole towards north of earth.
Place a small compass needle on a line drawn on a sheet of paper fixed on a drawing board. Rotate the board till the compass needle is parallel to the line. Now place a small bar magnet on this line with North Pole of the magnet pointing towards north of earth.
In the plot P and Q are two neutral points lying on the equatorial line of the magnet.
If d = distance of each neutral point from the centre of the magnet.
2l = magnetic length = Ns
M = magnetic dipole moment of the magnet, then magnetic field at each neutral point is
B2 = μ0 / 4π M/(d2 +l2) 3/2
At the neutral point field due to the magnet is balanced by horizontal component of earth’s field B2 = H
B2 = μ0 / 4π M / (d2 + l2) 3/2 = H
M= 4π (d2 + l2) 3/2 H / μ0
When magnet is short l2 < < d2
∴ M = 4π Hd2 / μ0
Magnet placed with its south pole towards north of earth.
Place the bar magnet on a sheet of paper in the magnetic meridian (as explained above) with its south-pole pointing towards north of earth. Plot the lines of force using the compass needle.
In this case, neutral points lie on the axial line of the magnet.
At each point intensity of magnetic field due to the magnet is
B1 = μ0 / 4π 2Md / (d2 + l2)2
As it is balanced by horizontal component of earth’s magnetic field (H) therefore
B1 = μ0 / 4π 2Md / (d2 – l2)2 = H
M = 4π H (d2 – l2)2 / 2μ0d
Hence magnetic dipole moment M of the bar magnet can be calculated.
When the magnet is short,
L2 << d2
∴ M = 4π Hd3 / 2μ0
In the two cases, the lines of force in the night boarhound of the magnet are mainly due to the magnetic field of the bar magnet, which is much stronger compared to the field of the earth however as we move away from the magnet field due to the magnet becomes weaker and earth’s field dominates. At large distance from the magnet the lines of force are almost straight and parallel directed from south to north. These linesrepresnt earths’s magnetic field.
From the two cases discussed above we find that when North Pole of a magnet is turned through 180the posit on of neutral points turns through 90 in the same direction. Hence in general when North Pole of magnet is tumid through θ digress the neutral points would turn through θ /2 in the same direction.
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