View Single Post
Mar28-12, 01:39 PM
PF Gold
fluidistic's Avatar
P: 3,207
1. The problem statement, all variables and given/known data
The problem can be found in Jackson's book, I think in chapter 1 problem 3 or something like this.
I must determine the charge distribution of a uniformly charged disk of radius R in spherical coordinates (I've done it in cylindrical coordinates and had no problem). The total charge is Q.
I've found a solution on the internet but the answer is different from mine.
I forgot to mention that I have to use Dirac's delta.

2. Relevant equations
[itex]\int _{\mathbb{R}^3} \rho (\vec x )=Q[/itex].

3. The attempt at a solution
Since the charges are over a 2d surface, there will be 1 Dirac's delta in the expression for rho, the charge density. I will use Heaviside's step function because the surface is limited.
Let [itex](r, \theta , \phi )[/itex] be the coordinates. I make the ansatz/educated guess that [itex]\rho[/itex] is of the form [itex]C \delta \left ( \theta - \frac{\pi }{2} \right ) \Theta (r \sin \theta -R)[/itex].
Integrating this distribution in all the space, I reach that C is worth [itex]\frac{3Q}{2\pi R^3}[/itex].
Therefore [itex]\rho (r, \theta )=\frac{3Q\delta \left ( \theta - \frac{\pi }{2} \right ) \Theta (r \sin \theta -R)}{2\pi R^3}[/itex].
However the solution provided on the internet is [itex]\rho (\vec x )=\frac{q }{\pi R^2r} \delta \left ( \theta - \frac{\pi }{2} \right ) \Theta (r -R)[/itex].
Are they both equivalent (I doubt it), if not, did I do something wrong? If so, what did I do wrong? Thanks a lot!
Phys.Org News Partner Science news on
Scientists develop 'electronic nose' for rapid detection of C. diff infection
Why plants in the office make us more productive
Tesla Motors dealing as states play factory poker