# Calculate the electric flux

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1. Mar 7, 2015

### hitemup

1. The problem statement, all variables and given/known data

The Earth possesses an electric field of (average) magnitude 150 N/C near its surface. The field points radially inward. Calculate the net electric flux outward through a spherical surface surrounding, and just beyond, the Earth's surface.

2. Relevant equations

Flux = EAcos(theta)

3. The attempt at a solution

I know that flux is proportional to the number of lines passing through a surface. Thus, we only need to calculate the the flux with respect to earth.

What confuses me is that, is there any net flux outward? Since the field lines point inward, and infinitesimally small surface vectors point outward, the sign of the flux will be negative. If the flux is negative, then there is a net flux into the volume. So I don't know if the answer is zero or simply (+-???)150*(4*pi*r^2), where r is the radius of the Earth.

2. Mar 7, 2015

### Xsnac

all the flux is outward on a closed surface. do you know gauss theorem ?

3. Mar 7, 2015

### hitemup

$$\Phi = \oint \vec{E}*d\vec{A}$$

$d\vec{A}$ always points outward from the enclosed surface.
So depending on $\vec{E}$, the flux can either be positive or negative?

4. Mar 7, 2015

### Xsnac

I'm not sure but I think that flux can eighter be 0 or positive . not negative.

5. Mar 7, 2015

### BvU

$\qquad$ no reason to shy away from what you deduced: $-$ 150*(4*pi*r^2)

This does represent a net outward flux, with a negative sign. Net in the scientific sense of non-zero(*). Like a net force can have a negative sign if the positive axis points the other way. Common language doesn't like that and claims that net outward has to be positive definite. Maybe that explains our hesitation.

(*) And even that isn't very scientific: net is net and doesn't say anything about the value; it can be zero just as well.

Last edited: Mar 7, 2015
6. Mar 7, 2015

### SammyS

Staff Emeritus
The flux can be and in this case is negative (outward). That's equivalent to saying that the net flux is inward.