Different equations for Electric Energy, me understand

AI Thread Summary
The discussion clarifies the difference between two equations related to electric energy. The first equation, U=E/Q, describes the potential energy of a charged particle in an external electric field, while the second equation, E=(QU)/2, pertains specifically to the energy stored in a capacitor. The confusion arises because both involve charged plates, but they refer to different contexts: one for a particle and the other for a capacitor's stored energy. The second equation is derived from the first by considering the work done to move a small charge within the capacitor. Understanding this distinction helps clarify the concepts of electric potential energy and stored energy in capacitors.
Armand1
Messages
2
Reaction score
0
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
 
Physics news on Phys.org


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.
 


Thanks voko, I think i got it!
 


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.
 
Kindly see the attached pdf. My attempt to solve it, is in it. I'm wondering if my solution is right. My idea is this: At any point of time, the ball may be assumed to be at an incline which is at an angle of θ(kindly see both the pics in the pdf file). The value of θ will continuously change and so will the value of friction. I'm not able to figure out, why my solution is wrong, if it is wrong .
TL;DR Summary: I came across this question from a Sri Lankan A-level textbook. Question - An ice cube with a length of 10 cm is immersed in water at 0 °C. An observer observes the ice cube from the water, and it seems to be 7.75 cm long. If the refractive index of water is 4/3, find the height of the ice cube immersed in the water. I could not understand how the apparent height of the ice cube in the water depends on the height of the ice cube immersed in the water. Does anyone have an...
Back
Top