## flux always zero

Anbousice
Posts: 1
Joined: Sun Jul 01, 2018 12:11 am

### flux always zero

I had a problem with a constant electric field and a arbitray shape, and we had to find the total flux. The answer was zero, but I don't see how we can know that. I can see why if it's a regular shape, but what if it is a weird shape? How can we know that it all cancels?

jeff
Posts: 38
Joined: Mon Mar 05, 2018 11:54 pm

### Re: flux always zero

Hi Anbousice,
Anbousice wrote:
Sun Jul 01, 2018 12:13 am
I had a problem with a constant electric field and a arbitray shape, and we had to find the total flux. The answer was zero, but I don't see how we can know that. I can see why if it's a regular shape, but what if it is a weird shape? How can we know that it all cancels?
It sounds like you would like a conceptual discussion instead of a calculation. If so, then I think the best way to think about this is by using the concept of electric field lines.

In that case, we can think of the electric flux as the total number of field lines going out of some shape (for positive flux) or going into the shape (for negative flux). If some lines are going out and some going in, then we find their difference to get the net flux.

Okay, since we have a constant electric field, the field lines are evenly spaced and they have no beginning or end. And our irregular shape has these field lines going through it.

Here's the main point: if we see a field line going into the shape (creating a negative flux), then if we follow it "forwards" at some point it has to leave the shape (creating a positive flux), right? If it didn't that would mean the field line ended inside the shape, which is not allowed for a constant electric field.

So no matter what the shape is, the number of times that a field line goes into the shape has to be exactly matched by the number of times the field lines go out, for a constant E field. So they exactly cancel!

As an example, look at the diagram below. The electric field lines (black arrows) enter the shape at fourteen points (red circles) and therefore leave the shape at fourteen points (green squares). And that's the way it always is for a constant electric field.

By the way, you can have zero net flux even if the field is not constant. Anytime the total charge is zero inside, the net flux will be zero. So if there is no charge at all, or equal amounts of positive and negative charge, the net flux will be zero.