Voltage of a point around an infinite long charged wire.

[null void]

Lets say i have a infinitely long wire with charge per length, λ and a point, p of a position with its closest distance to the wire is y. The wire extend infinitely parallel to X-Axis. How to determine the voltage at the position p?

Can i first regard the voltage contributed by a very small charge in this expression:

dV = κ(λ dx)/√(x² + y²) ...where κ = 1/4Ωε

v = κ(λ) ∫ dx/√(x² + y²)
= κλ ln( √(x² + y² + x)

If the integral start from -∞ to +∞ of x, the formula does not converge, but my logic tells me that the charge of the wire at infinity doesn't affect the voltage at point p. Does this mean my approach is wrong?

 

[jedishrfu]

Khan Academy has worked example of this problem that may help here:

https://www.khanacademy.org/science...age/a/ee-electric-field-near-a-line-of-charge