Why don’t two magnetic field lines intersect each other?

The principle that magnetic field lines do not intersect each other is a fundamental characteristic of magnetic fields and is derived from the nature of magnetic forces. There are two main reasons why magnetic field lines don’t intersect:

1. Directional Information:

Magnetic field lines represent the direction a small north magnetic pole would take if placed at any point in the field. If two magnetic field lines were to intersect, it would imply that at the point of intersection, the magnetic field has two different directions simultaneously. This is not physically possible because the direction of a magnetic field should be well-defined at every point. The tangent to a magnetic field line at any point indicates the direction of the magnetic field at that point.

2. Force on a Moving Charge:

Another way to understand why magnetic field lines don’t intersect is by considering the force experienced by a moving charged particle in a magnetic field. The force acting on a charged particle is perpendicular to both the velocity of the particle and the magnetic field direction (as given by the right-hand rule). If field lines were to intersect, it would imply that at the point of intersection, a charged particle could experience forces in two different directions simultaneously, violating the fundamental principles of electromagnetic interactions.
In summary, the non-intersecting nature of magnetic field lines ensures that the direction of the magnetic field is uniquely defined at every point in space. This property is consistent with the behavior of magnetic forces on charged particles and is a fundamental characteristic of magnetic fields.