How Does Electric Flux Change with Different Closed Surfaces Around Dipoles?

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SUMMARY

The discussion centers on the application of Gauss' Law to determine electric flux through various closed surfaces surrounding dipoles, each consisting of charges Q and -Q separated by distance d. The flux values of 8πkQ, 4πkQ, -8πkQ, -4πkQ, and 0 are analyzed in relation to the charge distribution within the surfaces. It is established that surfaces containing negative charges yield negative flux, while those with positive charges yield positive flux, indicating that the total flux through multiple surfaces does not simply add up due to the vector nature of electric fields.

PREREQUISITES
  • Understanding of Gauss' Law and its mathematical formulation.
  • Familiarity with electric dipoles and their charge distributions.
  • Knowledge of electric field directionality in relation to charge types.
  • Basic concepts of vector addition in physics.
NEXT STEPS
  • Study the implications of Gauss' Law in different geometrical configurations of charge distributions.
  • Explore the concept of electric field lines and their relationship to electric flux.
  • Investigate how to calculate electric flux for non-uniform charge distributions.
  • Learn about the applications of electric flux in electrostatics and capacitor design.
USEFUL FOR

Physics students, electrical engineers, and anyone interested in understanding electrostatics and the behavior of electric fields around dipoles.

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I have a figure showing two dipoles each having a Q and -Q charge with distance d separating the positive and negative of each dipole. The dipoles are then surrounded by multiple closed surfaces. I need to match fluxes of 8pikQ, 4pikQ, -8pikQ, - 4pikQ and 0 to these surfaces.


Gauss' Law states that flux=Eda=4(pi)kq for any closed surface


Since I have dipoles, my electric fields will be pulled toward the negative charge. THerefore, surfaces with negative charges in them should have a negative flux b/c the field points to the interior of the closed surface while my surfaces encompassing positive charges should have positive flux b/c the field points to the exterior of the surface. So, since each surface has a flux of 4pikq wouldn't the flux just keep adding up as the vector went through each additional surface?

thanks
 
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Could you post the figure?
 

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