Electric Potential Energy of a Rod

[SpringPhysics]

Homework Statement

There is a thin rod of
length L that carries a uniform charge per unit
length $$\lambda$$. Starting from the expression for the
potential of a point charge, derive an expression
for the electric potential V (y) at a distance y
away from the centre of the rod on the axis (y) of
the rod. Assume y > L/2.

Use this result to derive the y-component of
the electric field, Ey, along the axis of the rod,
for y > L/2.

Homework Equations

V(r) = Q/4$$\pi$$$$\epsilon$$r

$$\Delta$$V = - $$\int$$E$$\cdot$$ds

The Attempt at a Solution

I thought that the electric potential would be unchanged since the electric field is perpendicular to the displacement...

Or is this acceptable because the wire is not infinite?

 

[jbsteele]

V(y) = \lambda/4\pi\epsilon(L/2 - y)The electric field is then:Ey = - \partialV/\partialy= \lambda/4\pi\epsilon(L/2 - y)