Equipotential Lines: Can They Cross?

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SUMMARY

Equipotential lines cannot cross if they represent different potential values; however, they may appear to cross at saddle points where the potential value is equal. Field lines also do not cross except at singularities, such as point charges. The discussion highlights the relationship between electrostatic potential and complex functions, specifically noting that the real part of an analytic function can represent the potential while the imaginary part can represent field lines.

PREREQUISITES
  • Understanding of electrostatics and potential theory
  • Familiarity with saddle points in mathematical analysis
  • Knowledge of complex functions and their applications in physics
  • Basic concepts of electric field lines and their properties
NEXT STEPS
  • Study the properties of saddle points in potential theory
  • Learn about the relationship between electrostatic potential and complex analysis
  • Explore the implications of singularities in electric fields
  • Investigate the mathematical formulation of equipotential surfaces
USEFUL FOR

Physicists, electrical engineers, and students studying electrostatics or complex analysis who seek to deepen their understanding of equipotential lines and their properties.

mich_v87
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Is it possible for two different equipotential lines or two lines of force to cross ??
 
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mich_v87 said:
Is it possible for two different equipotential lines or two lines of force to cross ??

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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