# Electrostatics - line charges

## Homework Statement

A line charge has density λ and extends along the x axis from -a to +a. Find the electric potential at a point r on the x-axis (r>a). Use your result to find the E-field at r.

## Homework Equations

$$V = \frac{1}{4\pi \epsilon _0}\int\frac{dq}{r}$$

## The Attempt at a Solution

I've said so far:
dQ = λdx = Qdx/2a

Then I made the substitution into the above equation, and integrated wrt x with limits ±a, leaving me with $$\frac{Q}{4\pi \epsilon _0 r}$$.

However I'm not sure I made the correct integration here. I also believe that the answer for V should have λ in it somewhere. Have I gone wrong somewhere?

I haven't actually gotten round to looking at the E-field yet - I'll get there once this is completed!

Any pointers would be appreciated.

Thanks

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