Question

prof walter in his lecture said that field lines exist at each and every point which makes number of field lines passing through any surface infinte(as infinite points are present on any surface).
according to wikipedia electric flux is defined as follows
"Electric flux is proportional to the number of electric field lines going through a virtual surface."

so flux through any surface in any case should become infinite but in many problems we see that flux through any surface is finite quantity.can any one clarify me that how is this possible?

Answer 1

This can be possible for a certain reason. For an infinite number of field lines, the intensity of the electric field will decrease as the distance from the field source (the charge), but the area that the lines pass through will increase since they are spreading out at an EQUAL rate to the decrease in the field strength. Since flux = E*A, with E = electric field strength, and A the are that the lines passes through, the flux will be constant. A good example is with a point charge, in which the electric field strength varies inversely with r^2. Since the electric field lines radiate spherically, the are the lines will pass through will be a sphere, whose are varies directly with r^2. Thus, when we calculate the flux at ANY surface enclosing the field, the flux IS CONSTANT. It is true that the field lines exist everywhere, but the frequency of the field lines passing through a virtual surface only reveals RELATIVE ELECTRIC FIELD STRENGTH since the wikipedia statement in reality says that a surface with relatively more field lines passing through than another surface. Example: When drawing electric field lines, you can draw an infinite amount of electric field lines and still be considered appropriate for a certain charge q, but in the same diagram, you have two charges 2q and q, you MUST GIVE 2Q twice as much lines as Q. Conclusion: Flux is really only dependent on the field strength and virtual area, and although theoretically the field lines does exist in terms of infinite lines, the lines are there only to express RELATIVE FIELD STRENGTH as well as other conceptual ideas like the relative orientation of the area with the field on the flux.

Answer 2

thanks for taking so much time for my doubt dominusscholae but can you tell me what is the general theoretical meaning of flux of any quantity(i need meaning of flux in general but not electric flux in particular) and also how did scientists know that electric flux=E*A i mean how did they get this formula or idea??

Answer 3

The general meaning of flux is the rate of flow through a certain surface. It was used mostly in mass transfer problems to understand the rate of flow through virtual surfaces. The formula\[\int\limits_{?}^{?}F*da\] with F being any mathematical field line, and da the vector differential of area(the product of the differential of area and the normal vector of the surface used; so the vector area for a sphere would be , is the general formula for flux. In general, flux can also be a measure of the divergence of a field, or how much the field spreads out from its origin, as shown by Green's theorem. For instance take a surface with field lines passing through it. If more field lines pass out rather than enter, then it is a sign that the field has a positive divergence, and thus a positive flux. The opposite also applies. At the time, things such as electricity and magnetism showed similarities to a fluid. For example, scientists saw an electric current through a wire as analogous to water flowing through a pipe. So scientists used the water analogy to treat electromagnetism under some of the mathematical properties used in mass transfer, one of which was flux. Electric flux (E*A) was derived from the fact that the mathematical field used was just the electric field, and A was the area the electric field passed through.