## Using Gauss's law for a butterfly net

StarRope
Posts: 4
Joined: Fri Jun 08, 2018 2:30 pm

### Using Gauss's law for a butterfly net

I have the following problem with gauss's law and I want to verify my approach. I wasn't too sure on what formula to use in this problem.

A butterfly net is in a uniform electric field of magnitude E 3.0 mN/C. The rim, a circle of radius a 11 cm, is aligned perpendicular to the field. The net contains no net charge. Find the electric flux through the netting

The question is: Do I use Gauss's Law here?

Next question: If I do use that, do I use the area of the net's face in the formula?

StarRope
Posts: 4
Joined: Fri Jun 08, 2018 2:30 pm

### Re: Using Gauss's law for a butterfly net

well nvm, E is not given as a vector

jeff
Posts: 39
Joined: Mon Mar 05, 2018 11:54 pm

### Re: Using Gauss's law for a butterfly net

Hi StarRope,
StarRope wrote:
Fri Jun 08, 2018 2:33 pm
I have the following problem with gauss's law and I want to verify my approach. I wasn't too sure on what formula to use in this problem.

A butterfly net is in a uniform electric field of magnitude E 3.0 mN/C. The rim, a circle of radius a 11 cm, is aligned perpendicular to the field. The net contains no net charge. Find the electric flux through the netting

The question is: Do I use Gauss's Law here?

Next question: If I do use that, do I use the area of the net's face in the formula?
We don't actually need all of Gauss's law here; we just need the flux calculation formula (the "definition" of flux). So we can use:

Phi = E A cos(theta)

since E is a constant. (Gauss's law is the one that relates flux to the enclosed charge.)

The answer is yes to your second question. The problem asks for the flux through the netting; however, that has to be equal in magnitude to the flux through the "face" (the opening) of the net. (Whatever field lines pass through the face have to also pass through the netting.)

If they had told us the direction of E, we would be able to find the actual sign of the flux, but here they just want the magnitude so all that we need to know is that the field is perpendicular to the rim.

So yes, here use EAcos(theta).

StarRope
Posts: 4
Joined: Fri Jun 08, 2018 2:30 pm

### Re: Using Gauss's law for a butterfly net

I'm almost sure that the angle is 90 degrees because they say it is perpendicular. Am I right ?

jeff
Posts: 39
Joined: Mon Mar 05, 2018 11:54 pm

### Re: Using Gauss's law for a butterfly net

StarRope wrote:
Fri Jun 08, 2018 5:21 pm
I'm almost sure that the angle is 90 degrees because they say it is perpendicular. Am I right ?
That's right! That's why we have to find the flux through the opening of the net. We could not calculate the flux directly through the netting, because we don't know what angle the electric field makes with the netting material at different points, or what its area is.

So we use this "indirect" method of calculating the flux through the rim opening to get the answer. Does that make sense?

StarRope
Posts: 4
Joined: Fri Jun 08, 2018 2:30 pm

### Re: Using Gauss's law for a butterfly net

Yeah, it seems quite clear to me after thinking a bit. that would be it for now , thank you