Why is Electrical Potential Energy Dimensionally Inconsistent?

In summary, the equation for electrical potential energy in the case of two charges separated at a distance r is V=(q1q2)/(4*pi*epslion*r). This equation, while often written as V= Q/4pi*epslion*r in textbooks, still maintains dimension consistency. There may be confusion in deriving this equation from Coulomb's law, but it is still accurate. The equation V= \frac{Q}{4\pi \epsilon \,r} represents electrostatic potential at a point r from charge Q, while E= \frac{Q_1Q_2}{4\pi \epsilon \,r} represents the electrostatic energy of two charges Q_1 and Q_2
  • #1
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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  • #2
[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.
 

1. What is electrical potential energy?

Electrical potential energy is the energy that an electrically charged object possesses due to its position relative to other charged objects in an electric field.

2. Why is electrical potential energy important in science?

Electrical potential energy is important in science because it helps explain the behavior of charged particles and their interactions with one another. It is also a key concept in understanding electricity and magnetism.

3. What is dimensional inconsistency?

Dimensional inconsistency refers to a situation where the units of measurement for a physical quantity do not match up. In other words, the dimensions of the quantity on one side of an equation do not equal the dimensions on the other side.

4. Why is electrical potential energy dimensionally inconsistent?

Electrical potential energy is dimensionally inconsistent because it is measured in joules (J), which is equivalent to kg*m^2/s^2. However, in some equations, it is also represented as V*A (voltage times current), which has units of kg*m^2/s^3. This inconsistency occurs because electrical potential energy is derived from both electric potential (V) and electric field strength (E), which have different units.

5. How can we reconcile the dimensional inconsistency of electrical potential energy?

To reconcile the dimensional inconsistency of electrical potential energy, we can use the equation E = V/d, where E is the electric field, V is the electric potential, and d is the distance between the charged objects. This equation shows that electrical potential energy is directly proportional to electric potential and inversely proportional to distance. By using this equation, we can convert between the units of J and V*A and maintain dimensional consistency.

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