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Homework Help: Equipotential lines

  1. Oct 11, 2005 #1
    Is it possible for two different equipotential lines or two lines of force to cross ??
     
  2. jcsd
  3. Oct 11, 2005 #2

    vanesch

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    Ha, subtle. A priori, no, you'd think and in general this is correct. However, there can be saddle points and the potential line with the value equal to the potential of the saddle point will show a "crossing".
    However, clearly, potential lines with DIFFERENT potential values cannot cross. Idem for field lines (except of course at singularities, like point charges, where they all meet).

    Interesting thought:

    If V(x,y) is the (electrostatic) potential, then you can construct an analytic complex function V_c(x+i y) such that Re( V_c(x+i y)) = V(x,y) and Im(V_c(x+i y)) = constant gives you the field lines.

    cheers,
    Patrick.
     
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