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How did it get to that? Stretching Coulomb's law... 
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#1
Jun1311, 02:22 PM

P: 45

1. The problem statement, all variables and given/known data
The charge is distributed with uniform surface density σ on the disk of radius R. Find the potential at the axis of the disk. 2. Relevant equations Coulomb's law and the definition of a electric potential at point x 3. The attempt at a solution I have a solution in front of me but can't understand some step inside it: The potential can be defined now phi(x)= (1/4pi*epsilon0)Integral[(sigma(x')/xx')dS'] and the solution for the integral from 0 to R is: (sigma/2*epsilon0)(sqrt(x^2+R^2)z) Now, the electric field at this point is: E(z)=(sigma/2*epsilon0)(1(z/sqrt(z^2+R^2)) I can clearly follow until now, but then the book says that for z>>R we get E=Q/(4pi*epsilon0*z) where Q is the total charge of the disc. How can it be proportional to 1/z?? when I take z>>R  I get E(z)=0... 


#2
Jun1311, 02:52 PM

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#3
Jun1411, 12:44 AM

P: 45

2. what kind of a binomial expansion can I possibly make here? please direct me some more... 


#4
Jun1411, 04:09 AM

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P: 41,326

How did it get to that? Stretching Coulomb's law...
[tex]\sqrt{z^2 + R^2} = z\sqrt{1 + (R/z)^2}[/tex] Since R/z << 1, can you see how to use a binomial approximation now? 


#5
Jun1411, 05:58 AM

P: 45



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