Explain on Mapping of Magnetic Field due to a Bar Magnet - QS Study
QS Study

A bar magnet is placed on a plane sheet of a paper. A compass needle is placed near the north pole of the magnet. The north and south poles of the compass are marked by pencil dots. The compass needle is shifted and placed so that its south pole touches the pencil dot marked for north pole. The process is repeated and a series of dots are obtained. The dots are joined as a smooth curve. This curve is a magnetic line of force. Even though few lines are drawn around a bar magnet the magnetic lines exists in all space around the magnet.

Magnet placed with its north pole facing geographic north

A sheet of paper is fixed on a drawing board. Using a compass needle, the magnetic meridian is drawn on it. A bar magnet is placed on the magnetic meridian such that its north pole points towards geographic north. Using a compass needle, magnetic lines of force are drawn around the magnet. (Figure)

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The magnetic lines of force is due to the combined effect of the magnetic field due to the bar magnet and Earth. It is found that when the compass is placed at points P and P ‘ along the equatorial line of the magnet, the compass shows no deflection. They are called “neutral points.” At these points the magnetic field due to the magnet along its equatorial line (B) is exactly balanced by the horizontal component of the Earth’s magnetic field. (Bh)

Hence, neutral points are defined as the points where the resultant magnetic field due to the magnet and Earth is zero.

Hence, at neutral points: B = Bh

[(μ0/4π) x {M/(d22)3/2}] = Bh