Coulomb 's law

1. Aug 14, 2011

skp524

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) .

2. Aug 14, 2011

xts

$$V= \frac{Q}{4\pi \epsilon \,r}$$ 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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