In the next section, this will allow us to work with more complex systems. In the special case of a closed surface, the flux calculations become a sum of charges. Recall that when we place the point charge at the origin of a coordinate system, the electric field at a point P that is at a distance r from the charge at the origin is given byįigure 6.14 Flux through spherical surfaces of radii =0. To get a feel for what to expect, let’s calculate the electric flux through a spherical surface around a positive point charge q, since we already know the electric field in such a situation. Now, what happens to the electric flux if there are some charges inside the enclosed volume? Gauss’s law gives a quantitative answer to this question. Therefore, if a closed surface does not have any charges inside the enclosed volume, then the electric flux through the surface is zero. We found that if a closed surface does not have any charge inside where an electric field line can terminate, then any electric field line entering the surface at one point must necessarily exit at some other point of the surface. We can now determine the electric flux through an arbitrary closed surface due to an arbitrary charge distribution.

Apply Gauss’s law in appropriate systems.

Explain the conditions under which Gauss’s law may be used.

We calculate the electric flux through each element and integrate the results to obtain the total flux.By the end of this section, you will be able to: What happens if the electric field isn’t uniform but varies from point to point over the area ? Or what if is part of a curved surface? For a non-uniform electric field, the electric flux dΦ E through a small surface area d A is given by: Φ = E x A x cosφ (electric flux for uniform E, flat surface) For example, if we took a two-dimensional disc of unit radius, then its boundary would be a circle, and so S1 0 S 1 0 and so it.

We say that is closed if and only if 0 0 which is to say it has no boundary. We generalize our definition of electric flux for a uniform electric field to: Let be a smooth sub-manifold in Rn R n, i.e. This is for the area perpendicular to vector E. For a uniform electric field E passing through an area A, the electric flux E is defined as: Electric flux is proportional to the total number of electric field lines going through a surface.Įlectric flux depends on the strength of electric field, E, on the surface area, and on the relative orientation of the field and surface.

The density of these lines corresponds to the electric field strength, which could also be called the electric flux density: the number of “lines” per unit area.

Note that field lines are a graphic illustration of field strength and direction and have no physical meaning. In pictorial form, this electric field is shown as a dot, the charge, radiating “lines of flux”. Gauss’s law states that the net electric flux through any hypothetical closed surface is equal to 1/ε 0 times the net electric charge within that closed surface. Gauss’s law involves the concept of electric flux, which refers to the electric field passing through a given area. When the electric field, because of its symmetry, is constant everywhere on that surface and perpendicular to it, the exact electric field can be found. In its integral form, Gauss’s law relates the charge enclosed by a closed surface (often called as Gaussian surface) to the total flux through that surface. In electromagnetism, Gauss’s law, also known as Gauss’s flux theorem, relates the distribution of electric charge to the resulting electric field.

Electric flux equation closed surface