- #1
theowne
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Under the Gauss' law section of the book.
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?
εΦ = q
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.
Homework Statement
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?
Homework Equations
εΦ = q
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.
