# Homework Help: Parallel Component for E over charged disk

1. Mar 25, 2006

### Living_Dog

(NOTE: I am doing this to possibly re-enter a graduate program and earn a PhD. This is not being done for class.)

DJ Griffiths, Prob. 2.6, solved.

My question is about the parallel component of the $$\vec{E}$$-field. If you integrate over cylindrical coordinates, then by symmetry this component cancels as you integrate around $$\phi$$. So my question is about that integral - will it integrate to zero, or are we to ad hoc cancel the $$\phi = 0$$ term for $$dq$$ with the $$\phi = 180$$ term for $$dq$$?

Here is the integral as I set it up:

$$2\pik\sigma\int{\frac{s^2}{(z^2 + s^2)^{\frac{3}{2}}}}ds$$,

where $$s, \phi, z$$ are the cylindrical coordinates.

Oh, and yes, I did try $$s = z \cdot tan(\theta)$$

and get $$\int{\frac{1}{cos(\theta)}}d\theta$$ plus another term which is handleable.

Now that I think of it, the integral should integrate to zero since it is for the full disk, namely: $$0 < \phi < 2 \pi$$. So it should naturally integrate to zero. ...no?

Any help would be appreciated.
-LD

Last edited: Mar 25, 2006