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Electrostatics - line charges

  • Thread starter Brewer
  • Start date
  • #1
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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


[tex]V = \frac{1}{4\pi \epsilon _0}\int\frac{dq}{r} [/tex]


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 [tex]\frac{Q}{4\pi \epsilon _0 r}[/tex].

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
 
Last edited:

Answers and Replies

  • #2
212
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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?
 
  • #3
You could find the Electric field using gauss's law and then use E=-dV/dr to solve for V.
 

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