Why is Electrical Potential Energy Dimensionally Inconsistent?

AI Thread Summary
The discussion addresses the dimensional inconsistency in the equation for electrical potential energy, V=(q1q2)/(4*pi*epsilon*r), and contrasts it with the dimensionally consistent form, V=Q/(4pi*epsilon*r). The confusion arises from attempting to derive the potential energy equation from Coulomb's law, which leads to the inconsistent form. Participants emphasize the importance of checking dimensions, asserting that both forms ultimately convey physical meaning despite initial misconceptions. The conversation clarifies that the electrostatic potential and energy equations are indeed dimensionally consistent when properly analyzed.
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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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V= \frac{Q}{4\pi \epsilon \,r} is an electrostatic potential at the point r from the charge Q.
E= \frac{Q_1Q_2}{4\pi \epsilon \,r} is an electrostatic energy of two charges Q_1 and Q_2 at the distance r.

Check dimensions (units) again! They are consistent.
 
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