3.16 The Magnetic Field Lines

The magnetic field lines (magnetic lines of force) are a visual and intuitive realization of the unseen magnetic field. The field lines of magnetic field lines for both the bar magnet and  the current carrying conductor and an electric dipole are very similar. The curves are closed Gaussian surfaces. Unlike electric lines of force, the magnetic field lines do not indicate the direction of the force on a moving charge.

Properties of magnetic field lines

1. The magnetic field lines form closed loops
2. The tangent to the field line at a given point represents the direction of the net magnetic field B at that point.
3. The number of field lines crossing per unit normal area is a measure of the magnitude of the magnetic field B.

The magnetic field lines do not intersect. This is because, if they intersect, it would mean that at the point of intersection, the field can have two directions, which is impossible.

One can plot the magnetic field lines in a variety of ways. One way is to place a small magnetic compass needle at various positions and note its orientation. This gives us an idea of the magnetic field direction at various points in space.

The bar magnet as an equivalent solenoid

What is the equation for magnetic dipole moment m associated with a current loop?

m=NIA, where N is the number of turns in loop, I the current and A the area vector.

The resemblance of magnetic field lines for a bar magnet and a solenoid suggest that a bar magnet may be thought of as a large number of circulating currents in analogy with a solenoid. Cutting a bar magnet in half is like cutting a solenoid. We get two smaller solenoids with weaker magnetic properties. The field lines remain continuous, emerging from one face of the solenoid and entering into the other face. One can test this analogy by moving a small needle in the neighbourhood of a bar magnet and a current carrying solenoid and noting that the deflections of the needle are similar in both cases.

It can be shown that the magnitude of the axial field of a solenoid at a distance x from its center,

B=mu0/4pi x 2m/x3

This is also the far axial magnetic field of a bar magnet which one may obtain experimentally. Thus, a bar magnet and a solenoid produce magnetic field. The magnetic moment of  a bar magnet is thus equal to the magnetic moment of an equivalent solenoid that produces the same magnetic field.