Question Regarding Work Done By Capacitor

[verd]

...This isn't a homework problem or anything, I'm just a bit confused about this and have a test coming up. So any clarification would be greatly appreciated...

http://www.synthdriven.com/images/deletable/24-4.jpg

We were just recently introduced to the concept of electrostatic potential, and it was defined as U. However, when it comes to a capacitor, this quantity U pops up once again in the following equation:

$$U=\frac{1}{2}CV^2$$

Where U is explained as the total energy stored by the given capacitor...

Now, I know that U=-W. However, this phrasing has me confused. I know that the work is equivalent to the energy stored within a capacitor because the energy stored within the capacitor is the same as the amount of work done on the capacitor, right??

However, that formula doesn't seem to work in this situation because we're talking about a single test charge within the electric field of the capacitor... It's much more microscopic... So would I then use something like W=qV??

But even then, I need V, and in order to find V I'd need C...


I'm just a bit confused on how to go about this, I believe I'm confusing concepts, and any sort of explanation to sort this out would be greatly appreciated.

Thanks

 

[Päällikkö]

Indeed you are mixing up concepts, the total energy of the capacitor (the formula you have) has little to do with moving one point charge in the capacitor.
How does an electric field and the force exerted on the point charge relate?

 

[verd]

Well... Coulomb's law says

$$E=\frac{kq}{r^2}$$
$$F=\frac{kq_{1}q_{2}}{r^2}$$

And I know that
$$V=Ed$$

...Am I going in the right direction??

 

[Päällikkö]

Sort of.

I wouldn't use potential (V) in this problem. Again, how to relate E and F (you should see it from the equations you had in your last post, or think about the definition of a field)?

 

[Andrew Mason]

Well... Coulomb's law says

$$E=\frac{kq}{r^2}$$
$$F=\frac{kq_{1}q_{2}}{r^2}$$

And I know that
$$V=Ed$$

...Am I going in the right direction??

You would not use Coulomb's law here. Coulomb's law just gives you the electric field, or force per unit charge, of a point charge. But the field here is not that of a point charge. It is uniform and it is given to you.

I would start with: what is the definition of work?

AM

 

[verd]

Are you looking for E=Fq??

I mean I understand how to determine work given two point charges, but I've got something in between the plates of a capacitor... And I don't know the charge on the plates of the capacitor, it just know the field. So should I be looking for the charge on the plates of the capacitor?

 

[verd]

You would not use Coulomb's law here. Coulomb's law just gives you the electric field, or force per unit charge, of a point charge. But the field here is not that of a point charge. It is uniform and it is given to you.

I would start with: what is the definition of work?

AM

Work in a non-electrical sense is W=Fd
In an electrical sense, it's W=qV

...I just don't know how to think about this conceptually...

 

[Päällikkö]

Are you looking for E=Fq??

Well, almost: F = qE

I mean I understand how to determine work given two point charges, but I've got something in between the plates of a capacitor... And I don't know the charge on the plates of the capacitor, it just know the field. So should I be looking for the charge on the plates of the capacitor?

You know the strength of the field generated by the two charged plates. Using the equation above, you can determine the force exerted on the point charge/test particle.

I should've asked the definition of work first, as Andrew Mason pointed out. Now's the time to put the equation into use, though.

 

[Andrew Mason]

Work in a non-electrical sense is W=Fd
In an electrical sense, it's W=qV

...I just don't know how to think about this conceptually...

So, since electrical force = qE, you can express work as:

$$W = Fd = qEd$$

E = force per unit charge, q = charge, d = distance.

In this case, you are given E in terms of Energy per unit charge per unit of distance (which is just Force/unit charge).

So a coulomb of charge will gain 8 Joules if it moves one metre in that field. How much will 20e-6 Coulomb gain if it moves .05 m.?

AM

 

[verd]

Wow. Thank you. This makes sense.

Thanks for straightening me out. I appreciate it guys. Thanks again.