# Magnetic Field of a Dipole Bar Magnet

Consider a short bar magnet of magnetic moment $M$. Its magnetic field at a point P1 located at a distance $d$ in the axial direction (end position) is given by \begin{align} B_1 &=\frac{\mu_0}{4\pi}\frac{2M}{d^3}, \end{align}

The magnetic field at a point P2 located at a distance $d$ in the equatorial direction (broadside position) is given by from its centre is given by \begin{align} B_2 &=\frac{\mu_0}{4\pi}\frac{M}{d^3}. \end{align} Note that magnitude of $B_2$ is half of $B_1$.

## Drawing the magnetic lines of forces

Magnetic lines of forces indicates the direction of magnetic field in space. The magnetic lines of forces of a bar magnet can be easily drawn with a magnetic compass.

You need a bar magnet, magnetic compass, sheet of paper, and a pencil to draw the magnetic lines of forces.

Fix a white sheet of paper on a horizontal surface and keep a strong bar magnet on it. Place a small magnetic compass at various points near the magnet, and note the direction in which its needle comes to rest at these points. Figure shows these directions at points such as A, B, C, D, E and F. The direction of the needle at a point gives the direction of the magnetic field at that point.

Place the compass close to the north pole of the magnet. Once the needle comes to rest, look from above, and with a pencil, mark the position of the north pole of the needle on the sheet (i.e., mark the point closest to the north pole). Now, shift the compass ahead in such a way that after the needle comes to rest, its south pole is at the point marked for the previous position of the north pole. Mark the position of the north pole of the needle at the new location. Keep moving the compass ahead in this way till you reach the south pole of the magnet. Then join all the points marked on the paper with a smooth curve.

Repeat the whole process to get some more curved lines. Each time start from a new position near the north pole of the magnet. If you draw tangent at any point on these lines, the magnetic field at that point will be along the tangent.

A line such that the tangent at any point on it gives direction of the magnetic field at that point is called magnetic field line or magnetic line of force. Figure shows some magnetic field lines due to a bar magnet. An arrow showing the direction of the field at a point has been drawn on each field lines. Remember that the field lines are imaginary. They just help us visualize magnetic field.

You can see magnetic field lines with the help of iron fillings too. Place a glass or clear plastic sheet over a bar magnet. Sprinkle some iron fillings over the sheet, and gently tap the sheet. The iron fillings will arrange themselves to show the magnetic field lines.