Gauss's Flux Theorem

This is a page about Gauss's Flux Theorem. A work in progress by Jeff Patz

The Main Idea

Gauss's Flux Theorem is a way of relating charge distribution to its resulting electric field.

A Mathematical Model

In words, the electric flux of a closed surface is equal to the total charge enclosed in the closed surface over the constant epsilon naught. The electric flux of a closed surface is also equal to the surface integral of the electric field evaluated over the closed surface.

[math]\displaystyle{ \Phi_E = \frac{Q}{\varepsilon_0} = \oint_C E\bullet dA }[/math]

Where E is the electric field, dA is the infinitesimal area in the direction of the electric field, and the dot denotes a dot product.

For the special case of a constant electric field, the electric flux is equal to the electric field over the closed surface multiplied by the area and the cosine of the angle between the two vectors.

[math]\displaystyle{ \Phi_E = EAcos(\theta) }[/math]

Where E is the electric field, A is area of the surface, and /theta is the angle between the E and A

A Computational Model

How do we visualize or predict using this topic. Consider embedding some vpython code here Teach hands-on with GlowScript

Examples

One Surface and Uniform Electric Field

A disk of radius 5 meters is in an area of uniform electric field with magnitude 400 Volts/Meter. The angle between the electric field and the disk is 35 degrees.

Using the simplified version of Gauss's Law: [math]\displaystyle{ \Phi_E = EAcos(\theta) }[/math], fill out the known values, which in the case is all values needed.

[math]\displaystyle{ \Phi_E = EAcos(\theta) }[/math]

Connectedness

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History

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See also

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References

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