When to use PE = 1/2(QV) or PE = qV to find potential energy.

[MedicalMan14]

I do not understand what determines whether I should use one formula or the next. In the case of a charge moving from one pole to the other via a dialectric. Is it because it is a single charge I thus use "PE=qV" whereas if i was moving the entire dialectric then it would be PE = 1/2(QV). That is the only rationality I can muster.

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[TieuBachHo]

You are right. If it's a single charge, then PE = qV; otherwise, PE = 1/2 QV. The whole rationale behind it isn't quite diff. to grasp but it's rather lengthy to explicate. Just know that as more charges are being forced to separate onto the opp. plates, more energy is required as the resistence increases exponentially - like charges repel each others. If you translate this concept into a potential value, it makes sense to average out that potential value when you have multiple charges, just like when you take an average velocity.

For simplicity, that's exactly what you need to know for the purpose of the MCAT.

 

[MedicalMan14]

Hm ok that clarifies things slightly. However, I am confused, more energy is required to resist the movement of one charge from one plate to the next, or is that wrong?

 

[TieuBachHo]

Hm ok that clarifies things slightly. However, I am confused, more energy is required to resist the movement of one charge from one plate to the next, or is that wrong?

I am not sure what your take on that but let me put it this way. More energy is required to place an additional charge on the opposite plate - this is the stored energy due to the fact that like charges repel. The resistance comes from the opp. plate for an additional charge. For example, if you force a bunch of electrons onto a confined space, they tend to break away. So that means they will resist any futher effort of placing an additional electron on it. Does it make more sense?

 

[MedicalMan14]

I was not under the assumption that a capacitor stores particles of like charges together.

 

[Silverfalcon]

The way I was taught in class (I haven't looked at any MCAT for physics) is that PE = qV is a generic equation used for electric potential energy and its relation to electric potential (difference, if you had delta there).

On the other hand, PE = 1/2*Q*V is a special case applying to the capacitor. That's why PE = 1/2*(CV)*V = 1/2*CV^2, which is a form that I often used.

http://en.wikipedia.org/wiki/Capacitance

I just look at the problem and figure out what I need to know... I hate memorizing for physics since understanding is so much more fun. Good luck!

 

[MedicalMan14]

I agree thank you. I will research this more.

 

[TieuBachHo]

I was not under the assumption that a capacitor stores particles of like charges together.

A capacitor is just where you store charges for use when needed. Just do lil bit of research, it's quite easy to understand.

 

[kentavr]

Let's assume that you understand that PE=qV for one charge. Now, for condenser you can move one small charge(q) from plate to plate and work will be qV also. However, when you move the next charge(q2) the V is less, since you total charge on both plates are now Q-q. and so on. When you move the "last" charge V is almost zero. To find the total PE you need to sum all these works. (Integrate) or take the average which will be 0.5*QV (Note, I use the capital Q in this formula) HTH