How Do You Calculate Electric Potential and Field for a Finite Line Charge?

[Brewer]

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

 

[Brewer]

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?

 

[chaoseverlasting]

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