The reason is that the sources of the electric field are outside the box. The magnitude of the flux through rectangle BCKF is equal to the magnitudes of the flux through both the top and bottom faces. Here, the net flux through the cube is equal to zero. The net electric flux through the cube is the sum of fluxes through the six faces. The electric flux through the other faces is zero, since the electric field is perpendicular to the normal vectors of those faces. The electric flux through the top face ( FGHK) is positive, because the electric field and the normal are in the same direction. Electric flux through the bottom face ( ABCD) is negative, because E → E → is in the opposite direction to the normal to the surface. Notice that N ∝ E A 1 N ∝ E A 1 may also be written as N ∝ Φ N ∝ Φ, demonstrating that electric flux is a measure of the number of field lines crossing a surface.įigure 6.7 Electric flux through a cube, placed between two charged plates. Electric flux is a scalar quantity and has an SI unit of newton-meters squared per coulomb ( N We represent the electric flux through an open surface like S 1 S 1 by the symbol Φ Φ. The quantity E A 1 E A 1 is the electric flux through S 1 S 1. If N field lines pass through S 1 S 1, then we know from the definition of electric field lines ( Electric Charges and Fields) that N / A 1 ∝ E, N / A 1 ∝ E, or N ∝ E A 1. To quantify this idea, Figure 6.4(a) shows a planar surface S 1 S 1 of area A 1 A 1 that is perpendicular to the uniform electric field E → = E y ^. Again, flux is a general concept we can also use it to describe the amount of sunlight hitting a solar panel or the amount of energy a telescope receives from a distant star, for example. Similarly, the amount of flow through the hoop depends on the strength of the current and the size of the hoop. As you change the angle of the hoop relative to the direction of the current, more or less of the flow will go through the hoop. The numerical value of the electric flux depends on the magnitudes of the electric field and the area, as well as the relative orientation of the area with respect to the direction of the electric field.Ī macroscopic analogy that might help you imagine this is to put a hula hoop in a flowing river. 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.Figure 6.3 The flux of an electric field through the shaded area captures information about the “number” of electric field lines passing through the area. 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.

Electric flux formula