Electric flux – definition, formula

Electric flux – definition, formula – In this post, we will define electric flux and study its equation. We will also study a few figures that come with numerical problems related to electric flux. Later, we will find the statement of Gauss’ theorem.

Electric Flux – definition

Definition of flux: The total number of electric field lines crossing a surface normally is called electric flux.

Electric flux can also be defined as the surface integral of the Electric Field over the entire closed surface.

Electric Flux equation | formula of electric flux

Formula or equation of electric flux: The electric field through surface element dS is ΔΦ = E.dS = E dS cos θ, where E is the electric field strength. (see figure 1)

electric flux definition, ΔΦ = E.dS = E dS cos θ
figure 1: electric flux ΔΦ = E.dS = E dS cos θ

The surface integral form of the flux formula is this: ΦE = ʃA E. ds

This can be expanded as ΦE = ʃA E. ds = ʃA E ds cos θ = ES cos θ

When, θ = 0° i.e., when the area vector and the electric field vector are parallel, then ΦE = ES

Here, S = surface area.

[ Note: The area vector is normal (perpendicular) to the surface]

θ in the electric flux equation

θ is the angle between the direction of the Electric field E and the normal to the surface being considered.

In other words, θ is the angle between the direction of the Electric field E and the area vector.

[ Note: The area vector is normal (perpendicular) to the surface]

How to quickly find this θ from a given figure or diagram when solving numerical problems?

θ = the minimum angle by which we have to rotate the surface plane to make it normal to E field line direction= minimum angle by which we have to rotate the E field line direction to make it normal to the Surface.

We will do this quick check because the definition of flux considers only the electric field lines crossing a surface normally. [normal means perpendicular]

finding flux from figures

See figure 2.

figure 2: How flux can be calculated

flux In figure 2 (i):

θ = angle between the direction of the Electric field E and the normal to the surface being considered = 0°.

In other words, the minimum angle by which we have to rotate the E field line direction to make it normal to Surface = 0°.

Hence, flux Φ = E . A = EA cos 0° = EA

flux In figure 2 (ii):

θ = angle between the direction of the Electric field E and the normal to the surface being considered.

In other words, minimum angle by which we have to rotate the E field line direction to make it normal to Surface = θ

Hence, flux Φ = E . A = EA cos θ

flux In figure 2 (iii):

θ = angle between the direction of the Electric field E and the normal to the surface being considered = 90°.

In other words, minimum angle by which we have to rotate the E field line direction to make it normal to Surface = 90°.

Hence, flux Φ = E . A = EA cos 90° = EA

Gauss’s Theorem statement

It states that the total electric flux through a closed surface is equal to 1/ε0 times the net charge enclosed by the surface.

Also read: Derivation of Gauss’ Theorem

Electric flux – definition, formula
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