Gauss Law
elGauss’ Law
AP Physics C
Electric Flux
Let's start be defining an area on the surface of an object. The magnitude is “A” and the direction is directed perpendicular to the area like a force normal.
A
E
Flux ( or FLOW) is a general term associated with a FIELD that is bound by a certain AREA. So ELECTRIC FLUX is any AREA that has a ELECTRIC FIELD passing through it.
We generally define an AREA vector as one that is perpendicular to the surface of the material. Therefore, you can see in the figure that the AREA vector and the Electric Field vector are PARALLEL. This then produces a DOT PRODUCT between the 2 variables that then define flux.
Electric Flux
The electric field lines look like lines of a "fluid". So you can imagine these lines are flowing (even though nothing is really flowing). The word FLUX roughly means FLOW. So based on this idea we can define the ELECTRIC FLUX as the ELECTRIC FEILD through a SURFACE AREA. Since the area vector is defined as perpendicular to the surface and the electric field goes through it, we define this equation as a dot product, similar to the work function.
Φ E = E • A = EA cos θ dΦ = ∫ Eda
A differential amount of flux is the cross product between the electric field and a differential amount of area. Since you want the total flux, you integrate to sum up all the small areas. Thus the TOTAL FLUX is found by integrating over the ENTIRE SURFACE. The circle on the integration sign simply means the surface is CLOSED!!.
∫
Electric Flux
Visually we can try to understand that the flux is simply the # of electric field lines passing through any given area.
In the left figure, the flux is zero.
In the right figure, the flux is 2.
• When E lines pass outward through a closed surface, the FLUX is positive • When E lines go into a closed surface, the FLUX is negative
Electric Flux
What is the electric flux of this cylinder?
Φ E = ∑ Φ = Φ1 + Φ 2 + Φ 3 , E = constant, A1 = A2 Φ E = EA1 cos 0
AP Physics C
Electric Flux
Let's start be defining an area on the surface of an object. The magnitude is “A” and the direction is directed perpendicular to the area like a force normal.
A
E
Flux ( or FLOW) is a general term associated with a FIELD that is bound by a certain AREA. So ELECTRIC FLUX is any AREA that has a ELECTRIC FIELD passing through it.
We generally define an AREA vector as one that is perpendicular to the surface of the material. Therefore, you can see in the figure that the AREA vector and the Electric Field vector are PARALLEL. This then produces a DOT PRODUCT between the 2 variables that then define flux.
Electric Flux
The electric field lines look like lines of a "fluid". So you can imagine these lines are flowing (even though nothing is really flowing). The word FLUX roughly means FLOW. So based on this idea we can define the ELECTRIC FLUX as the ELECTRIC FEILD through a SURFACE AREA. Since the area vector is defined as perpendicular to the surface and the electric field goes through it, we define this equation as a dot product, similar to the work function.
Φ E = E • A = EA cos θ dΦ = ∫ Eda
A differential amount of flux is the cross product between the electric field and a differential amount of area. Since you want the total flux, you integrate to sum up all the small areas. Thus the TOTAL FLUX is found by integrating over the ENTIRE SURFACE. The circle on the integration sign simply means the surface is CLOSED!!.
∫
Electric Flux
Visually we can try to understand that the flux is simply the # of electric field lines passing through any given area.
In the left figure, the flux is zero.
In the right figure, the flux is 2.
• When E lines pass outward through a closed surface, the FLUX is positive • When E lines go into a closed surface, the FLUX is negative
Electric Flux
What is the electric flux of this cylinder?
Φ E = ∑ Φ = Φ1 + Φ 2 + Φ 3 , E = constant, A1 = A2 Φ E = EA1 cos 0