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If we have a bar magnet and we break it as shown below

Then as per the image we get two bar magnets But does this happen instantaneously or there is some time lag between this process.
Or simply, Can magnetic monopoles exist even for a short time period?

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As long as the two parts are together, and the boundary is not a physical separation, you may consider them as one magnet or as two. There is no difference as the two poles you inserted cancel out and nothing is created. Of course when you pull the two parts things happen but the poles already existed in this sense.

Magnetic monopoles are incompatible with electromagnetic field theory in its present form.

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  • $\begingroup$ Does it happen with solenoid also? $\endgroup$ – Abhishek May 26 '18 at 10:38
  • $\begingroup$ Yes there is no difference. $\endgroup$ – my2cts May 26 '18 at 19:23
  • $\begingroup$ A pole is just a location on a surface where field lines leave (N) or enter (S). The pole type therefore depends on what you call inside or outside. $\endgroup$ – my2cts May 27 '18 at 10:23
  • $\begingroup$ what is problem with magnetic monopoles $\endgroup$ – Abhishek May 27 '18 at 10:25
  • $\begingroup$ There is no problem as they do not exist, not in experiment and not in the theory of electromagnetism as used in the context quantum mechanics and quantum field theory. Of course you can think of adding a source term to Gauss's law of magnetism, but this will make it impossible to describe EM with a single four potential. This four potential description is essential to the Schrödinger equation and generally to Lagrangian and Hamiltonian mechanics, which are foundations of QM and QFT. $\endgroup$ – my2cts May 27 '18 at 11:11

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