# A sphere of uniform charge

1. Oct 6, 2009

### theowne

Under the Gauss' law section of the book.

1. The problem statement, all variables and given/known data
As you penetrate a uniform sphere of charge, E should decrease as less charge is inside the sphere, while E should increase because you are closer to the center of this charge. Which effect dominates?

2. Relevant equations
εΦ = q

3. The attempt at a solution

This is what I was thinking, maybe I'm completely misguided. q = charge density * 4/3 pi r^3 so q decreases by a factor of r^3. From gauss law' E = q / ε 4 pi r^2. So E decreases with q which decreases by r^3 while E increases with r^2 factor due to the denominator. So I would guess that q is the dominant factor there. Would it be a saisfactory answer if I just did [charge density * 4/3 pi r^2] / [ε 4 pi r^2] = (charge density * r) / (3 ε) = E so in the end as r decreases the E field will decrease.

2. Oct 6, 2009

### Delphi51

Looks great to me! E decreases linearly as r decreases.