Different equations for Electric Energy, me understand

[Armand1]

I've been reading recently about Electric Potential Energy and when introduced with the following situation of two charged plates (one (-) and the other (+)) and a charged particle between them I've been taught the following equation.

a) U=E/Q ⇔ E=QU

However now when I'm reading about a capacitor the equation for the stored electric energy in the capacitor is

b) E= (QU)/2

But how is this possible? A capacitor is to my understanding exactly what I've described above, two charged plates. So how come there is a different equation for the same thing?

For references I've read equation a) in Heureka A page 215 and b) in Heureka B page 180. The books are written in Swedish. I am very grateful for any help I can get to help me understand.

P.S I've been searching for the same question without luck so I believe it was appropriate to post this thread

 

[voko]

These two equations do not describe the same thing. The first one describes the potential energy of some particle (of charge Q) in some external electric field. The second describes the energy stored in a capacitor; Q is the charge stored in that same capacitor, not of some unrelated particle.

 

[Armand1]

Thanks voko, I think i got it!

 

[voko]

Very well. Keep in mind, though, that the second equation is obtained from the first one. It is done by considering some small charge dq that has to be moved from one plate to another. Assuming that the capacitor already holds some charge q, the potential difference is u = q/C; the energy required to move the small charge dq from one plate to another is then dE = u dq = q dq/C; this is the first equation. Integrating this we obtain E = Q^2/(2C) = QU/2.

 

[Nickie]

I can provide an explanation for the different equations for electric energy in this situation. The first equation (a) is the equation for electric potential energy, which is the energy that a charged particle possesses due to its position in an electric field. This equation shows that the electric potential energy (U) is equal to the electric field (E) multiplied by the charge (Q) of the particle. This equation is used when considering the energy of a single charged particle in an electric field.

On the other hand, the second equation (b) is the equation for the stored electric energy in a capacitor. A capacitor consists of two conductive plates separated by a dielectric material. When a voltage is applied to the plates, they become charged with opposite charges. The energy stored in a capacitor is equal to the work done to charge the capacitor, which is given by the equation E = (1/2)QU. This equation takes into account the fact that the capacitor has two plates and the energy is shared between them, hence the factor of 1/2.

Therefore, the two equations are not contradictory but rather represent different concepts. Equation (a) is for the energy of a single charged particle, while equation (b) is for the energy stored in a capacitor. It is important to note that both equations are valid and can be used depending on the specific situation being considered. I hope this helps clarify the confusion.