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Continuity of Magnetic Field Lines

I was taught in school that magnetic lines can not cross each other without breaking. Also i was taught that magnetic field lines are unidirectional traveling out of the north end of the magnetic field and connecting to the south magnetic pole. My question is, In the event of the lines being broken, would the broken or open north magnetic lines coming out of the north pole of the magnetic field( traveling at the speed of 186,000 miles per second, the speed of light) be able to connect with any other south magnetic poles they encounter even a second or more away.thank you, Ron G.

 

Diagram of Earth's magnetic field lines includ...

 

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