Neutral Points

Neutral Points

The magnetic field around the magnet is the resultant of the field of the magnet and horizontal component of the earth’s magnetic field when a bar magnet is placed in the flat position on a horizontal table.

Determining Neutral Points

The magnetic lines are drawn on a horizontal paper by using a compass needle. Starting from N-pole of the magnet and marking by pencil dots on the position of the compass needle, we will get a number of the field lines.

Along the axis of the magnet, the earth’s horizontal component and magnetic field strength of bar magnet are in opposite direction but on the sides, two fields are in the same direction. The field intensity of bar magnet is stronger near the poles and weaker at farther from the poles and the earth’s horizontal component is constant. At positions marked as X on the axis, the magnetic field intensity of bar magnet and the horizontal component of the earth’s magnetic field are exactly equal but opposite. So the resultant field intensity at these points is zero.

A point in the magnetic field of a bar magnet at which the resultant field intensity is zero is called neutral point.

Here

$$\begin{align*} (B – H) &= 0 \\ \text {or,} \: B &= H \\ \text {or,} \: \frac {\mu _0}{4\pi } \frac {2Md}{(d^2 – l^2)^2} &= H\\ \text {or,} \: M &= \frac {4\pi }{\mu _0 } \frac {(d^2 – l^2)^2}{2d} H \\ \text {If the magnet has very short length, then} \\ M &= \frac {2\pi }{\mu _0} d^3 H \\\end{align*}$$

The magnetic field lines when the magnet is placed with its N-pole pointing to north direction are shown in figure. In this case, two fields are opposite in the direction to each other at two sides of the magnet and the neutral points are obtained there on the axial line.

$$\begin{align*} \text {At these points}, \\ R &= H \\\text {or,} \: \frac {\mu _0}{4\pi } \frac {M}{(d^2 + l^2)^{3/2}} &= H \\ \text {or,} \: M &= \frac {4\pi (d^2 + l^2)^{3/2} }{\mu _0 } H \\ \text {If the magnet has very short length, then} \\ M &= \frac {4\pi }{\mu _0} d^3 H \\ \end{align*}$$

The neutral point can be obtained where the magnet is placed with the N-pole point pointing to east or west. Magnetic lines of force can be drawn around the magnet and derive the ratio M/H at the neutral point.