Electric field of a uniformly charged disk

Woopydalan

Hello,

I am looking at an example of finding the charge of a uniform disk with a continuous charge on the surface.

They go about the problem by finding the infinitesimal charge of concentric rings

dq = σdA = σ(2πr dr)

The part I don't understand is that they use the area as 2πr dr? The area of a ring would be ∏(R2^2 - R1^2), right?

jtbell

Correct, that's the exact area of the ring. However, if dr = R2 - R1 is small, the other formula is a very good approximation, which gets better and better as dr becomes smaller and smaller. To see this, let R2 = R1 + dr in the equation above, cancel out whatever you can, and then drop any terms with (dr)^2. Those terms become negligible compared to terms with just dr, when dr is very small.

Woopydalan

Ok I just calculated it and now I see. The book didn't even bother to explain that approximation, which left me confused. Thank you for clearing that up so quickly =)