[Physics] Can the magnetic lines of force of two or more magnets intersect each other

electric-fieldselectromagnetismmagnetic fieldsvirtual-particles

Basic property of magnetic lines of force is that, they can never intersect each other. Among the two points given below, which one is correct?

  • Magnetic lines of force of same magnet can't intersect each other, but magnetic lines of force of different magnets can intersect each other.
  • Magnetic lines of force can't intersect each other irrespective of their origin (i.e whether the lines were of same magnet or different magnets, they can't intersect)

Suppose I have two bar magnets. If I tend to make the repelling poles join together by exerting force (i.e, if I tend to make north pole of two magnets, or south pole of two magnets join together). Would the magnetic lines of force intersect each other?

Best Answer

Here are from wikipedia drawings of the field lines of two magnets in two orientations, like-like, like-unlike .

 poles like like

North pole to north pole

like unlike

North pole to south pole.

The lines distort but do not intersect.

These field lines are solutions of the formal Maxwell differential equations. Differential equations do not give discontinuous solutions, as would be the case if two lines crossed. Discontinuities in the solutions when smooth boundary conditions exist are not possible, as in the drawings. Discontinuities can exist as singularities, which can only exist at the source of the field. The field lines themselves follow smooth functions away from sources.

Mawell's equations have been continually validated by an enormous number of experiments and applications and thus we trust the descriptions of nature that the solutions give.