# Help understanding the units in Gauss's law

1. Jan 17, 2009

### goldenwest

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

Well, here's the homework question:

A charge Q is located inside a rectangular box. The electric flux through each of the six surfaces of the box is: phi1=+1500Nm^2/C, phi2=+2200Nm^2/C, phi3=+4600Nm^2/C, phi4=-1800Nm^2/C, phi5=-3500Nm^2/C, and phi6=-3400Nm^2/C. What is Q?

My guess is that I will have to use Gauss's law (electric flux = enclosed charge over electric constant) to find out the charge for each number and then find the mean of all the charges? But what's really confusing me is that Gauss's law's units don't seem to cancel out properly. Please show me why I'm an idiot.

2. Relevant equations

seems like it should be

...why isn't it?

3. The attempt at a solution
My attempt at a solution would be
+1500 * 8.99E9 = 1.35E13
+2200 * 8.99E9 = 1.98E13
+4600 * 8.99E9 = 4.14E13
-1800 * 8.99E9 =-1.62E13
-3500 * 8.99E9 =-3.14E13
-3400 * 8.99E9 =-3.06E13

The mean of those numbers = -5.83E11 = Q?

2. Jan 17, 2009

### LowlyPion

3. Jan 17, 2009

### goldenwest

Okay so $$(\sum\phi)\epsilon = Q$$? Q = -2.16E13?

4. Jan 17, 2009

### LowlyPion

Are you sure that's the sum of the Φ ?

5. Jan 17, 2009

### goldenwest

Oops, -3.60E12.... but am I doing it correctly now?

6. Jan 17, 2009

### LowlyPion

So correctly that it looks like you got it right.

7. Jan 17, 2009

### goldenwest

Okay, thank you very very very very much. I'm still confused about why the units work out that way - could you explain that to me?

8. Jan 17, 2009

### LowlyPion

ε is in units of C²/Nm²

Φ is in units of Nm²/C

Q is in units of C

Edit: Sorry. I posted the units of Coulombs Constant which is the inverse.

Last edited: Jan 17, 2009
9. Jan 17, 2009

### goldenwest

Yes, I know. I know this is probably a stupid question... please bear with me.

$$\stackrel{Q}{\overline{\epsilon}} = \stackrel{C}{\overline{Nm^{2}C^{-2}}} = \stackrel{C^{3}}{\overline{Nm^{2}}}$$

Why is that wrong?

10. Jan 17, 2009

### LowlyPion

Sorry. I posted the units of Coulombs Constant which is the reciprocal of the units of ε.

I corrected my error.

http://en.wikipedia.org/wiki/Electric_flux

11. Jan 17, 2009

### goldenwest

Oooooooooook, now I understand. Thank you very much for all your help!

12. Jan 17, 2009

### goldenwest

So was I using the wrong constant when solving for the problem.... meaning I got the answer wrong? I was using 8.99E9. Should I be using 8.85E-12?

13. Jan 17, 2009

### LowlyPion

Yes. I missed that too I guess. I should have checked it.

εo is what you want, and not k.

14. Jan 17, 2009

### goldenwest

Thanks again, you have been extremely helpful.