Electric Fields and Gauss' Law

[kristi.lynn]

I need some guidance if anyone can help me!

1. A small cube of volume 8.0 cm^3 is .30 cm from a metal sphere that has charge 2.00uC. If the cube is empty, what is the total flux through it?

I tried finding the flux of the sphere as if it was a point charge but I don't know where to go from there or even if there is right.

2. a) At a distance of .200 cm from the center of a charged conducting sphere with radius .100 cm, the electric field is 480 N/C. What is the electric field .600 cm from the center of the sphere?
b) At a distance of .200 cm from the axis of a very long charged conducting cylinder with radius .100 cm, the electric field is 480 N/C. What is the electric field .600 cm from the axis of the cylinder?
c) At a distance of .200 cm from a large uniform sheet of charge, the electric field is 480 N/C. What is the electric field 1.20 cm from the sheet?

Ok that's the second rather long question, so first I did a bunch of work for part a and now I'm thinking maybe I didn't have to do any work bc isn't the electric field the same outside of the object everywhere? I don't know though I'm all confused and TA's are not cool to teach physics with calculus. So if anyone can help me before tomorrow morning I'd love it...

Thanks all..

-kristi.lynn

 

[Doc Al]

Welcome to PF!

All of these problems are straightforward applications of Gauss's law. What have you tried so far?

If you show your work, we can find out where you got stuck. If you haven't a clue, start by stating Gauss's law. (Look it up!)

 

[kristi.lynn]

Ok here's what I tried for 1 I went with Flux=integral of E da and got as far as the flux was 2.3 x 10^5 for the sphere, then I didn't even know why I got the flux at all... I'll look at Gauss' Law again I guess..

Other question, what is the value of epsilon naught? Because I know that q(enclosed)/epsilon naught is gauss' law too but she never told us the value..best I could come up with is like 8.8x10^-12 just using 1/4piEo = 9.0x10^9... would that be right?

For the second problem, I still don't know if my thinking that the electric field is the same everywhere was right, but I tried doing this

E=kq/r^2 and I used r as the distance between the outside edge of the sphere and the spot they said had E=480 and found q=5.3 x 10^-14 then I used that q to do E=kq/r^2 for the distance .00500m bc that is the distance between the end of the sphere and the point where I'm looking for E..

I don't know if any of this work is right but if I'm on the right track please let me know..

Thanks for the quick reply!

-kristi.lynn

 

[Doc Al]

Ok here's what I tried for 1 I went with Flux=integral of E da and got as far as the flux was 2.3 x 10^5 for the sphere, then I didn't even know why I got the flux at all... I'll look at Gauss' Law again I guess..

Gauss's law relates the the total flux through any closed surface to the charge contained within that surface:
$$\Phi = q/\epsilon_0$$
For question 1: what's the charge in that empty cube? So what's the flux through it?

Other question, what is the value of epsilon naught? Because I know that q(enclosed)/epsilon naught is gauss' law too but she never told us the value..best I could come up with is like 8.8x10^-12 just using 1/4piEo = 9.0x10^9... would that be right?

Yes...
$$\epsilon_0= 8.85E{-12} \frac{C^2}{Nm^2}$$
and, yes:
$$\frac{1}{4\pi\epsilon_0} = k = 8.99E9 \frac{N m^2}{C^2}$$

For the second problem, I still don't know if my thinking that the electric field is the same everywhere was right, but I tried doing this

No. For each part, draw a Gaussian surface with the right symmetry. Then use Gauss's law to find the electric field.

 

[kristi.lynn]

So even though there's a charged sphere like 3 cm away it doesn't affect the flux on the cube all because it's empty. So I had to kinda put a Gaussian surface around the box, not the sphere... That's good to know...

and for the Second one the work I did already was wrong too huh? I'll have to work on that one... Thanks again for your help.

-kristi.lynn

 

[kristi.lynn]

hey I think I got part a of the second one...I'm so dumb all I had to do was make the distances be the radii of the gaussian surface right? and then I got the charge based on the first length, then I got the second E with the charge...I really think I got it! Awesome :) now on to cylinders! Hey if you have time for another question...know how with cylinders and with sheets of charge there's a lamda and a sigma (respectively in the equations? I know they are the charge per unit length / or per unit area but how do I know what it is if it just says the cylinder is "very long" or the sheet is "very large?" Do I need to use a limit or something? I don't really see any examples in the book. I'm so happy I got one! yay! Thanks!

-kristi.lynn