an electrostatic field line is a continous curve i.e. a field line cannot have sudden breaks.why not?

Answer 1

An electrostatic field is a conservative field. This means that the change in potential energy resulting from moving between two points in the field only depends on the points and not on the path taken between them. This is supported by experimental evidence.

The change in potential energy between two points is proportional the number of field lines crossed while moving between them, taking the lines' direction into account. (This is a simplification, but it's a close analogy.)

Now imagine that one of the field lines had a break in it. What would happen when if you moved between two points, A and B on either side of the line? (Imagine the field is on a two-dimensional surface for now.) Well, the answer would depend on the path you took. You could go straight across the line, crossing one field line. Or you could go round the end of the break, crossing no field lines. So your change in potential energy would depend on the path you took, which contradicts the experimental evidence. Therefore the field lines can't have breaks in them.

To describe the situation more correctly mathematically, you can say that the change in potential energy is the line integral of the electrostatic field along the path you take. Another way of stating this is that the electrostatic vector field is the gradient field of a scalar potential energy field. (This is another definition of a conservative field). If the field lines had breaks in them, this would mean that the potential energy field would be undefined (not infinite!) at the breaks, contradicting the assumption that the field is conservative.

Answer 2

An electrostatic field line if discontinuous quicker or later the tangent to the curve at that element is purely no longer defined that still will recommend that, th electric powered field at5 that element isn't defined. yet that's not a threat for any distribution of costs.

Answer 3

If it did have a sudden break, then it would mean that the potential at that point is infinite.

Answer 4

potential is deriative of field.
if in some point a line suddenly breaks it means that the potential at this point is infinite

Answer 5

it can't break because its an intangible force

Answer 6

continuity would be broken,or power would be deverted.