# Calculating density charge with and EF

1. Aug 25, 2009

### Luchopas

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

Problem : Supose that there is a solid sphere of radius R , with density charge thats depends of the distance to the centre of the sphere ( p = p(r)) :

Question: supose that we know the electric field inside the sphere that is:

http://img175.imageshack.us/img175/3237/dibujowks.jpg" [Broken]

where A and b are postive constants. Calculate the density charge inside the sphere and the electric field outside the sphere.

Last edited by a moderator: May 4, 2017
2. Aug 25, 2009

### nicksauce

Do you know any equations that might be useful in relating charge density and electric field?

3. Aug 25, 2009

### gabbagabbahey

Well, you know what the electric field inside the sphere is, so why not start by using Gauss' law (in differential form!) to find the charge density there,,,,

4. Aug 25, 2009

### Luchopas

why in differential form????

5. Aug 25, 2009

### nicksauce

The differential form gives you $\rho$ directly! The integral form gives you $\int \rho dV$. Since $\rho$ is what you're looking for, surely you must agree that the differential form is the best way to go.

6. Aug 25, 2009

### Luchopas

ok perfect this is what i did:

http://img440.imageshack.us/img440/2251/dibujoxzv.jpg" [Broken]

Last edited by a moderator: May 4, 2017
7. Aug 25, 2009

### gabbagabbahey

You seem to have dropped the factor of $\frac{1}{\epsilon_0}$ when you replaced (2) in (1)

8. Aug 25, 2009

### Luchopas

mmm.... i think is correct...

9. Aug 26, 2009

### gabbagabbahey

mmm...I don't....

what happened to the $\frac{1}{\epsilon_0}$ that was part of your expression for $E$?

10. Aug 26, 2009

### Luchopas

SORRY YOU ARE RIGHT , is the same formula but without the epsilon 0.

thats was for part a) , now for calulating the E.F for outisde the sphere i got this:

http://img36.imageshack.us/img36/8785/dddv.png" [Broken]

for this i dont know how to solve the integration.. please help...!

Last edited by a moderator: May 4, 2017
11. Aug 26, 2009

### nicksauce

It's just an exercise in integration by parts. First work out $\int xe^{-x}dx$, then x^2 and x^3.

12. Aug 26, 2009

### Luchopas

ok i have done it , but besides the integration do you feel my answer is correct?

thanks

13. Aug 26, 2009

### gabbagabbahey

looks fine to me.

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