Electric field generated from dipoles

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SUMMARY

The discussion focuses on the electric field generated by electric dipoles, which consist of a positive and a negative charge separated by a finite distance. It clarifies that while point charges at the same location would cancel each other out, the finite separation in dipoles leads to a non-canceling effect in the electric field. Mathematically, the example provided illustrates that the fields do not cancel when considering the distances involved, specifically using the expressions \(\frac{1}{x-\epsilon}\) and \(-\frac{1}{x+\epsilon}\).

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  • Understanding of electric dipoles
  • Basic knowledge of electric fields
  • Familiarity with mathematical concepts involving limits
  • Knowledge of point charge behavior in electrostatics
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  • Study the mathematical derivation of electric fields from dipoles
  • Learn about the superposition principle in electrostatics
  • Explore the concept of electric field lines and their representation
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I'm having a little difficulty understanding the electric field generated from electric dipoles. As far as I know electric fields are generated on positive charges and terminated on negative charges. Since a dipole is a positive charge and a negative charge separated by a very small distance, why doenst they just simply cancel each other out?

Thanks
René
 
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If the positive and negative charge were point charges at exactly the same location then they would cancel out. However, if the separation between them is finite (but as small as you like) then the cancellation is not exact.

Mathematically, it's like this:

\frac {1}{x} and - \frac {1}{x} cancel exactly when added together (we ignore x = 0 for this discussion) but \frac {1}{x-\epsilon} and -\frac {1}{x+\epsilon} do not cancel.
 

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