Calculating density charge with and EF

[Luchopas]

Homework Statement

Problem : Supose that there is a solid sphere of radius R , with density charge that's 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"

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

 

[nicksauce]

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

 

[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,,,,

 

[Luchopas]

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,,,,

why in differential form?

 

[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.

 

[Luchopas]

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.

ok perfect this is what i did:

http://img440.imageshack.us/img440/2251/dibujoxzv.jpg"

 

[gabbagabbahey]

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

 

[Luchopas]

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

mmm... i think is correct...

 

[gabbagabbahey]

mmm...I don't...

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

 

[Luchopas]

mmm...I don't...

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

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"

for this i don't know how to solve the integration.. please help...!

 

[nicksauce]

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

 

[Luchopas]

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

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

thanks

 

[gabbagabbahey]

looks fine to me.