# Find the Potential as a function of position

## Homework Statement

A rod of length L carries a charge Q uniformly distributed along its length. The rod lies along the y-axis with one end at the origin. Find the potential as a function of position along the x-axis

## Homework Equations

$$dV=\vec{E}\cdotp d\vec{l}$$

$$V=\frac{kq}{r}$$

## The Attempt at a Solution

I think I am to use the first equation posted, but I am not sure how to relate it to the x-axis, if the rod lies along the y-axis. Also, what is the displacement here? I am assuming it is just dy?

Andrew Mason
Homework Helper

## Homework Statement

A rod of length L carries a charge Q uniformly distributed along its length. The rod lies along the y-axis with one end at the origin. Find the potential as a function of position along the x-axis

## Homework Equations

$$dV=\vec{E}\cdotp d\vec{l}$$

$$V=\frac{kq}{r}$$

## The Attempt at a Solution

I think I am to use the first equation posted, but I am not sure how to relate it to the x-axis, if the rod lies along the y-axis. Also, what is the displacement here? I am assuming it is just dy?
You have to integrate along the rod from y = 0 to +L.

$$V(x) = \int_{0}^{L} \frac{k}{r}dq$$

Work out the expression for dq in terms of dy. Work out the expression for r in terms of x and y (think: Pythagoras).

AM

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