Electric potential of a line of charge

[channel1]

Homework Statement

Find the electric potential at a point d perpendicular to one end of a line of charge with a positive uniform linear charge density lambda, length L, and negligible thickness.

Homework Equations

EdA=q/ε_0
A = 2πdL
V_f - V_i = -integral(Eds)

The Attempt at a Solution

for E i get λ/(2πDε_0) by drawing a gaussian cylinder around the line of charge and then i plug that into the integral for V which turns into V = Ed*ln|(L+(d^2+L^2 )^(1/2))/d|

the answer i get is V= λ/(2πε_0 ) ln|(L+(d^2+L^2 )^(1/2))/d| which is correct except that i should have a 4πε_0 instead of a 2πε_0 but i don't understand why since the area of my gaussian cylinder is 2πdL

 

[davo789]

Are you *sure* the area is 2*pi*d*L?

 

[channel1]

...yes? lol i mean the way i drew my diagram charge would only be coming out of the middle of the cylinder. i mean i acknowledge that I am making a mistake somewhere in there but i can't for the life of me see why.

 

[SammyS]

Gauss's Law isn't applicable here.

There's not sufficient symmetry.

What is the electric potential at a distance R from a point charge with a charge of Q ?