Is electric potential always continuous in an electrostatic field? I mean, does it suffer from discontinuity at any point?
Potentials are defined up to an additive constant. This means that there is a certain freedom in the value it takes. What I believe is done is that this constant is defined depending on the system of study, so that it is continous. The reason why we do this is contained in this post:
A clue: What relation is there between the electrostatic potential and field?
Roughly speaking, yes, it's always continuous in an electrostatic field. However, the electric potential at the point where the electric field source(charge) occupies is not defined.Is electric potential always continuous in an electrostatic field? I mean, does it suffer from discontinuity at any point?
What if E vector is discontinuous at one point?To make its concept clear, we need to look at the definition of the electric potential.
v = -∫Edl
Obviously, if E vector, the electric field, exists, then we can know the difference of electric potential between the given two points. Next, we let the electric potential at one point be any number we want. So, we get the electric potential at the another one point.
If you can find an integral path where links the desired point and the point given its electric potential and where E vector is well-defined, then you can calculate the electric potential of the desired point.What if E vector is discontinuous at one point?