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Electric field and Laplace's equation

  • Thread starter Void123
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  • #1
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Homework Statement



I have to show for a conducting sheet bent along one axis into the shape of a wedge, with a certain angle, that the magnitude of the electric field in the bend is proportional to [tex]r^{(\pi/\theta) - 1}[/tex], where theta is the opening angle.


Homework Equations





The Attempt at a Solution



I'm not sure how to treat this problem, is this just separation of variables for Laplace's equation in three dimensions?
 

Answers and Replies

  • #2
674
2
You can use separation of variables for Laplace's equation in cylindrical coords. You also know the potential won't have any 'z' dependence so that will simplify your work.
 
  • #3
141
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I know what the solution is, but I don't really understand the physical logic behind it.

If [tex]V(s,\phi) = V_{0} + B_{0}Ln s + \Sigma (s^{n}[A cos (n\phi) + B sin (n\phi)] + s^{-n}[C cos (n\phi) + D sin (n\phi)]) [/tex]

Now, I know that at z = 0 this forces [tex]B_{0}, C, and D[/tex] to go to zero (or else there will be infinite terms), but I don't understand necessarily why. What forces us to conclude, considering cylindrical symmetry, that s -> 0?
 
  • #4
674
2
Don't forget you have boundary conditions you need to satisfy.
 
  • #5
141
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Okay, thats what I thought. But which boundary conditions are those if they are not specified in the problem?
 
  • #6
674
2
They are specified in the problem. What do you know about potentials and conductors.
 

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