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Why cant a field line have sudden breaks?
they can have sudden "breaks" in the sense that they can be discontinuous over a certain distance..for example, consider a conducting sphere, there are no field lines inside the sphere, but the lines emerge from the surface of the sphere...
however, in d general sense, there can b no break as this would imply that the influence of a charge has suddenly become zero at that point, which is not possible as the influence of any charge extends upto infinity..
there are however, other ways of explaining this
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