- #1
jimmyoung
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Homework Statement
I am trying to derive an expression for the potential of a positive point charge by bringing in another positive test charge in from infinity to a point at a distance R from the point charge.
Homework Equations
$$V_f - V_i = - \int \vec E \cdot d \vec r \, dr$$
The Attempt at a Solution
Being that the test charge is coming in from infinity ##\vec E \cdot d \vec r = Edrcos180 = -Edr##
So then $$V_f - V_i = \int E \, dr$$
Then taking ##V_i = 0## at infinity
$$ V= \frac q {4\pi\epsilon_o}
\int_\infty^R \ {r^{-2}} \, dr =
\left. - \frac q {4\pi\epsilon_o r} \right|_\infty^R$$
This gives me ##V = - \frac q {4\pi\epsilon_o R}##
Which is almost right except I have that negative sign that says the potential is decreasing...
I thought since the potential is taken to be 0 at infinity and that the test charge is getting closer to the charge I would get a positive result saying the potential is increasing.
Could someone help explain why I got this negative result?