Eletric potential created by a homogenously charged disc

1. Dec 1, 2013

victorcell

1. The problem statement, all variables and given/known data

I've to demonstrate the electric potential that a charge q feels when it's broght from infinite to a point z. The problem is that every demonstration i found out there starts with the definition of potential eletric as dV = k. dq/ r²; but i cannot use that, 'cause my professor wants us to go with delta V = - integral ( E. dl). no problem to find the eletric field though. The issue regard the integral

2. Relevant equations

After the integration, when dealing with the limits, infinite and z, the result comes down to + and - infinite, which is clearly an indertermination mathematicaly speaking, in spite of that, if i'm allowed to cancel that out, the result is just perfect. I am posting the picture of what i've done, i've canceled the infinites justifying by the definition of electric potential been zero at r=infinite; but i am not sure that this is allowed.. thanks for the help

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2. Dec 1, 2013

TSny

Hello, victorcell. Welcome to PF!

To handle the limit of the integral at z = ∞, you need to evaluate $$\lim_{z \to \infty} (\sqrt{z^2+R^2} - z)$$

Last edited: Dec 1, 2013