# 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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## Answers and Replies

Is this correct? I've spent my morning researching this, and I can't seem to find anything to compare it to - I'm a little confused as to what to do when the point is somewhere on the same line. Are my limits correct?

You could find the Electric field using gauss's law and then use E=-dV/dr to solve for V.