Question about the E-field along center axis of charged ring

[Loopas]

http://www.physics.udel.edu/~watson/phys208/exercises/kevan/efield1.html

I'm having trouble understanding the derivative notation. I know that "dE" and dQ" have to do with the derivative, but what exactly does that mean in the context of this problem? For some reason I find it difficult to understand why this derivative notation is used in so many physics questions. How do I know what variables have derivative notation?

 

[tiny-tim]

Hi Loopas!

I'm having trouble understanding the derivative notation. I know that "dE" and dQ" have to do with the derivative, but what exactly does that mean in the context of this problem? … How do I know what variables have derivative notation?

It isn't a derivative … in fact, you're going to integrate it.

dq is the charge on a tiny piece of the ring.

This is a standard procedure: you split the body into slices that are so small that you can regard all measurements on them as constant.

(for example, if you know the density of a body as a function of position, you say consider a small element of volume dxdydz, it can be assumed to have a constant density ρ, so the mass is ρdxdydz, and the total mass is ∫ ρdxdydz)

In this case, the charge is dq, the total charge is ∫ dq, the E_x for that charge is kxdq/(x²+a²)^3/2, and so the total E_x is ∫ kxdq/(x²+a²)^3/2


(btw, in this case, all measurements on the small charge really are constant, so ther's actaully no assumption here … but usually there is)