# Internal energy of dielectric

I have a plate capacitor with a given charge. It is then dipped in a dielectric fluid and I must determine which height the fluid reaches (all the necessary parameters are given). I can solve this problem if I make the following assumption: the polarization of the dielectric does not( or approximately does not) change its internal energy.

Is this a reasonable assumption? If so why?

• This problem is somewhat worked out in Griffith's EM book, but I think he uses a solid being pulled into a capacitor rather than a liquid. The same arguments should apply though. – Aaron Stevens Aug 2 '18 at 14:21

Polarization could cause a small increase in the internal energy of the fluid, due to the same processes that cause dielectric losses observed in capacitors, transmission lines, etc.

Polarization would result in a slight increase in the fluid temperature and slight increase in the potential energy of the polarized molecules, stretched by the electric field.

You will decide if this increase is negligible.

• Ok. I guess I am meant to assume it is negligible since otherwise more information would be needed to solve the problem( i think) – fibo11235 Aug 2 '18 at 16:51
• @fibo11235 Makes sense to me. – V.F. Aug 2 '18 at 17:27

What exactly is the internal energy of the dielectric? Does this actually decrease here?

A simpler way of looking at the situation is that the dielectric fluid rises so it gains gravitational potential energy. The work to do this comes from the energy stored in the electrostatic field between the capacitor plates, which falls. (The capacitor has been disconnected from the battery, so the charge on the plates is constant. See Energy Stored in a Capacitor with and without Dielectric.)

$$\text{decrease in energy stored in the capacitor = work done against gravity}$$

• Yes this is how I solved the problem. But this assumes that the work done on the fluid by the capacitor manifests itself completely as the rise in gravitational potential energy. I thought it was possible that the polarization maybe gives rise to some other energy stored in the fluid. – fibo11235 Aug 2 '18 at 18:09
• @fibo11235 ok, I misunderstood the point of your assumption. – sammy gerbil Aug 2 '18 at 18:32