Generating Expressions For Electric Flux

TSny

Wkipedia says "The electric flux through any closed surface is proportional to the enclosed electric charge". How much charge is enclosed in your closed surface?

Bashyboy

There isn't any charge within the closed surface; only electric fields pass through the surface.

TSny

That's right. Since Gauss' law states that the total flux through the closed surface is proportional to the charge within, what can you deduce about the value of the total flux?

Bashyboy

That the amount of electric field lines entering the surface is proportional to amount leaving. So the two expressions will be the same. How can I show this mathematically?

TSny

There's not much to do mathematically.

Fill in the blanks below:

Gauss' law says that the net flux through any closed surface equals the charge enclosed divided by ε_o. Since there's no charge enclosed, the net flux through the closed surface is _____________.

Since the flux through the curved part of the surface is _____________, the flux through the flat disk is _____________.

Bashyboy

The net flux through the surface would be zero. Webassign accepted my answer to the first question, but it didn't accept for the second one. For part b), was I supposed to put a negative symbol in front of what I put in for part a), and that would be the answer?

TSny

Yes. Total flux is zero. So, flux through curved surface + flux through flat surface = 0

Hence, flux through flat surface = - flux through curved surface.