To my knowledge, flux of a vector field through a given surface is the integral of the dot product of vector field and a unit vector given to a surface element over the entire surface. Field line is a curve such that vector at a point on it is tangent to the curve. But only a few field lines are drawn to help visualise the field and they are deliberately drawn such that the field strength is indicated by degree of closeness of lines.(right?) And I also believe that these principles are applicable in any vector field ( not just electric or magnetic field)
Now my question is that how come the number of field lines passing through a surface is proportional to the flux ? I want to clarify that my question is not in the sense that in reality there should be infinite field lines as in the case of some previously answered questions I have seen. My question is that how, from the definitions known to me as stated above, the following fact can be concluded.
P.S. Could somebody also tell if the facts known to me are correct?