# Getting weird formula for Capacitance

1. Dec 20, 2011

### lluke9

Okay, so I know
$$C=Q/ΔV$$

And ΔV is the sum of the electric fields multiplied by the distance between the charges, so if the first charge has a charge of Q and the other has -Q with R distance between, the electric potential/voltage is:
$$ΔV = [(kQ/r^2) + (kQ/r^2)]R$$
so
$$ΔV = 2kQ/R$$.

And $$C = Q/ΔV$$
so...
$$C = Q/(kQ/R)$$
and...
$$C = R/2k$$
and...
$$C = R/2[1/(4Πε_0)]$$
and
$$C = 2ΠRε_0$$

What...?
It would make some semblance of sense if R were inversely proportional to capacitance, but it isnt...

Last edited: Dec 20, 2011
2. Dec 20, 2011

### Staff: Mentor

Where ΔV is the voltage between two conductors.

That's only true if the field is constant.

Not sure what you're doing here with two point charges.

In any case: In the expression for the field from a point charge, r is the distance from the charge. So r for one charge is different than the r for the other. Also, the field isn't constant, so you can't just multiply by the distance R.

3. Dec 20, 2011

### lluke9

Well, I was just adding up the electric fields and doing V = EΔd...

But I'm guessing that's not possible because the electric field isn't constant...?

Okay, please forget about everything I typed up there, I guess it was a complete waste of time.

So how DO you change the voltage in a capacitor? Wouldn't it be to just increase the charge?
Actually, how do you FIND the voltage in a capacitor? Is it V = EΔd, because the electric field is constant in a capacitor?

4. Dec 20, 2011

### Staff: Mentor

You charge a capacitor by hooking it up to voltage source (a battery, perhaps). The higher the voltage, the greater the charge stored on each conductor.
For a parallel plate capacitor, the field is constant. So you could use that method.

5. Dec 20, 2011

### lluke9

So could you substitute for voltage in the capacitance equation?

$$C = q/EΔd$$

Then $$E_T$$ would be:
$$E_T = kq/r^2 + kq/r^2$$
because
$$E = kq/r^2$$
and both electric fields are going the same direction.

And then I'd arrive at the same thing I did in my original post...

$$E_T$$ = net electric field

6. Dec 20, 2011

### Staff: Mentor

That's the field for a point charge. Nothing to do with the constant field found between the plates of a parallel plate capacitor.