Why is Electrical Potential Energy Dimensionally Inconsistent?

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SUMMARY

The discussion centers on the dimensional consistency of electrical potential energy equations, specifically V=(q1q2)/(4*pi*epsilon*r) and V=Q/(4pi*epsilon*r). The latter is dimensionally consistent, while the former raises confusion regarding its physical meaning despite appearing inconsistent. The participant seeks clarity on deriving these equations from Coulomb's law, F=kq1q2/r^3, and questions potential misconceptions. Ultimately, the dimensions of both equations are confirmed to be consistent upon review.

PREREQUISITES
  • Understanding of Coulomb's Law and electrostatic forces
  • Familiarity with electrical potential and energy concepts
  • Knowledge of dimensional analysis in physics
  • Basic grasp of electrostatics and charge interactions
NEXT STEPS
  • Study the derivation of electrostatic potential from Coulomb's Law
  • Learn about dimensional analysis techniques in physics
  • Explore the implications of dimensional consistency in physical equations
  • Review the principles of electrostatics and energy calculations
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Students of physics, educators teaching electrostatics, and professionals involved in electrical engineering who seek to deepen their understanding of potential energy and dimensional analysis in physical equations.

skp524
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In the case of two charges separarted at a distance r, the electrical potential energy follows that V=(q1q2)/(4*pi*epslion*r), I want to ask why the dimenision of this equation is not consistent and this equation still has a physical meaning. From a textbook about electricity and magnetism, the equation is often in a form like V= Q/4pi*epslion*r, however, this equation has a dimension consistency . I am confused because initially I want to derive this equation from the common form of Coulombs' law ( F=kq1q2r/|r|^3), but if I follow this form, it would probably give the former equation that is not dimensionally consistent. I wonder if I got any misconception(s) .
 
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[tex]V= \frac{Q}{4\pi \epsilon \,r}[/tex] is an electrostatic potential at the point [itex]r[/itex] from the charge [itex]Q[/itex].
[tex]E= \frac{Q_1Q_2}{4\pi \epsilon \,r}[/tex] is an electrostatic energy of two charges [itex]Q_1[/itex] and [itex]Q_2[/itex] at the distance [itex]r[/itex].

Check dimensions (units) again! They are consistent.
 

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