If a conductor like copper is placed between two plates of a parallel plate conductor,neither touching any of them, what will happen to the capacitance of the capacitor?


Suppose you have a parallel plate capacitor:

Parallel plate capacitor

So we have a capacitance:

$$ C = \frac{\varepsilon_0 A}{d} $$

and a charge $Q$ on the plates given by:

$$ Q = CV $$

Suppose we now insert a sheet of copper in between the plates as you describe:


The electrons in the copper plate are free to move, so they flow towards the positive plate and you end up with two capacitors with an increased capacitance:

$$ C' = \frac{\varepsilon_0 A}{d'} $$

The combined capacitance is obtained by using the equation for two capacitors in series:

$$ \frac{1}{C_{tot}} = \frac{1}{C_1} +\frac{1}{C_2} $$

So in this case the new capacitance is:

$$ C_{tot} = \frac{\varepsilon_0 A}{2d'} $$

And since the copper sheet has a thickness greater than zero $2d' \lt d$ and therefore when you increase the copper sheet the capacitance increases.

  • $\begingroup$ so, is there a difference when we use a dielectric medium and a conducting medium with no contact with the plates of the capacitor? $\endgroup$ – pooza Jan 22 '17 at 12:41

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.