Electromagnetism: charge density

[Jalo]

Homework Statement

Given a sphere of radius R with a volumic charge distribution p find the function p.
The electric field inside of the sphere is radial with a constant modulus E

Homework Equations

div E = p / ε

∫∫E.ds = 1/ε * ∫∫∫ p * dV

The Attempt at a Solution

I tried to solve it using those two equations. (r is the radius)

div E = p / ε ⇔ dE/dr = p/ε ⇔ ∫dE = 1/ε ∫p dr ⇔ E = 1/ε * p * r ⇔
⇔ p = E*ε / r

I don't think I can integrate p like that, since p is a function of the radius. I don't know what to do thought..

Using the second equation and solving in a similar way I get:

∫∫E.ds = 1/ε * ∫∫∫ p * dV ⇔ E*4*pi*r^2 = 1/ε * p * (4/3)*pi*r^3 ⇔
⇔ p = 3*E*ε/rThe correct result would have been p = 2*E*ε / r

Any help would be appreciated!
Thanks.
Daniel

 

[chakra007]

Homework Statement

Given a sphere of radius R with a volumic charge distribution p find the function p.
The electric field inside of the sphere is radial with a constant modulus E

Homework Equations

div E = p / ε

∫∫E.ds = 1/ε * ∫∫∫ p * dV

The Attempt at a Solution

I tried to solve it using those two equations. (r is the radius)

div E = p / ε ⇔ dE/dr = p/ε ⇔ ∫dE = 1/ε ∫p dr ⇔ E = 1/ε * p * r ⇔
⇔ p = E*ε / r

I don't think I can integrate p like that, since p is a function of the radius. I don't know what to do thought..

Using the second equation and solving in a similar way I get:

∫∫E.ds = 1/ε * ∫∫∫ p * dV ⇔ E*4*pi*r^2 = 1/ε * p * (4/3)*pi*r^3 ⇔
⇔ p = 3*E*ε/r


The correct result would have been p = 2*E*ε / r

Any help would be appreciated!
Thanks.
Daniel

they usually tell the function of (ρ) rho, volume charge dis... and find the totale charge... use the equation Q = ∫∫∫ρdv , dv is easy to find even they don't tell... but they not even tell the function of Q ! if they did , may be use dQ/dv=ρ.
And the electric field to the center of the sphere is 0 , no matter of volume charge dis.. or surface charge dist... if the electric field to other point than center , it's much more complex... use the equation dE = kρdv/r^2 , k=1/4∏ε =contante
so Ez =∫∫∫dE cosθ =0
Ey=∫∫∫dE cosθcosα =0
Ex=∫∫∫dE cosθsinα =0
so E =0 to the center of sphere...