Gauss's Law

Electric Flux

Think of air blowing in through a window. How much air comes through the window depends upon the speed of the air, the direction of the air, and the area of the window. We might call this air that comes through the window the "air flux".

We will define the electric flux for an electric field that is perpendicular to an area as

= E A

If the electric field E is not perpendicular to the area, we will have to modify this to account for that.

Think about the "air flux" of air passing through a window at an angle . The "effective area" is A cos or the component of the velocity perpendicular to the window is v cos . With this in mind, we will make a general definition of the electric flux as

= E A cos

You can also think of the electric flux as the number of electric field lines that cross the surface.

Remembering the "dot product" or the "scalar product", we can also write this as

= E A

where E is the electric field and A is a vector equal to the area A and in a direction perpendicular to that area. Sometimes this same information is given as

A = A n

where n is a unit vector pointing perpendicular to the area. In that case, we could also write the electric flux across an area as

= E n A

Both forms say the same thing. For this to make any sense, we must be talking about an area where the direction of A or n is constant.

For a curved surface, that will not be the case. For that case, we can apply this definition of the electric flux over a small area A or A or An.

Then the electric flux through that small area is and

= E A cos


= E A

To find the flux through all of a closed surface, we need to sum up all these contributions of

over the entire surface,

We will consider flux as positive if the electric field E goes from the inside to the outside of the surface and we will consider flux as negative if the electric field E goes from the outside to the inside of the surface. This is important for we will soon be interested in the net flux passing throught a surface.

Homework Assignment

Gauss's Law

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(c) Doug Davis, 2002; all rights reserved