Register to reply 
Divergence in spherical polar coordinates 
Share this thread: 
#19
Aug1911, 06:26 AM

Sci Advisor
Thanks
P: 2,497




#20
Aug1911, 06:31 AM

HW Helper
P: 6,188

I suspect you're referring to Maxwell's law that says:
[tex]\textrm{div }\vec E = \frac {\rho} {\epsilon_0}[/tex] The divergence of a spherically symmetric charge is zero everywhere except at the place where the charge actually is. A point charge is a special case, since the charge density would be infinite (actually a Dirac deltafunction). In practice the charge would take in a certain volume. The divergence of the electric field is not zero at the place where the charge density is not zero. 


#21
Aug1911, 08:58 AM

P: 162

So can I go one more step and state that, at the points in space where the charge 'is' the electric field can no longer be defined by the function [itex]\frac{1}{r^2}[/itex][itex]\hat{r}[/itex] ?



#22
Aug1911, 09:44 AM

HW Helper
P: 6,188

Correct.
In the case of a solid sphere with constant charge density within, the electric field is proportional to [itex]r \hat {\boldsymbol r}[/itex] (inside the sphere). 


#23
Aug1911, 10:08 AM

P: 162

thank you, this helped a lot



Register to reply 
Related Discussions  
Divergence and curl of spherical polar coordinates  Calculus & Beyond Homework  0  
Divergence in spherical coordinates  Differential Equations  7  
Deriving the divergence in polar coordinates  Calculus & Beyond Homework  0  
Divergence in Polar Coordinates  Calculus & Beyond Homework  1  
Proof of Divergence Formula in Spherical Coordinates  Calculus & Beyond Homework  2 