# Homework Help: Question about inserting a dielectric material inside a capacitor

1. Jul 25, 2011

### pc2-brazil

I am self-studying "Physics" (Volume 3) by Halliday, Resnick and Krane, and would like to ask some questions regarding the following example given in the book (with solution). I will copy the entire example here, with solution (translated from Portuguese, because I am using a Portuguese translation of this book):

"A parallel plate capacitor, whose capacitance C0 is 13.5 pF, is subject to a potential difference of 12.5 V between its plates. The battery is turned off and a porcelain blade (κe = 6.5) is put between the plates (filling the space between the plates). What is the energy stored in the system, before and after the introduction of the porcelain?

The initial stored energy is given by $U_i = \frac{1}{2}C_0V^2$ = 1055 pJ.
The final energy is $U_f = \frac{q^2}{2C} = \frac{q^2}{2\kappa_eC_0} = \frac{U_i}{\kappa_e}$ = 162 pJ.

The final energy is less than the initial energy by a factor of 1/κe.
The "missing" energy is due to the fact that the capacitor exerted a force on the blade, doing work given by:
$W = U_i - U_f$ = 1055 pJ - 162 pJ = 893 pJ.
If the only force applied to the blade is the one exerted by the capacitor (ignoring all additional forces, such as friction), it will oscillate between the plates of the capacitor. The capacitor + blade system has a constant energy of 1055 pJ; the energy also oscillates between kinetic energy of the moving blade and energy stored in the electric field. In the instant in which the oscillating blade completely filled the space between the plates of the capacitor, its energy would be 893 pJ."

I would like to see if I understood the explanation above.
When it says "the capacitor exerted a force on the blade", does it mean that the blade is being attracted by the plates by electrostatic induction, that is, the capacitor is inducing a non-uniformly distributed charge on the blade during its insertion between the plates?
When it says "it will oscillate between the plates of the capacitor", does it mean that, if the plate is abandoned, partially inserted between the plates of the capacitor, it will perform an oscillatory movement parallel to the plates?

2. Jul 26, 2011

### SammyS

Staff Emeritus
The material of the blade will be electrostatically polarized.

Yes, the blade's oscillatory motion is parallel to the plates.

3. Jul 26, 2011

### ehild

In the real life, you will not see a blade oscillating forever between the plate of a capacitor. Part of the energy of the electric field is consumed for polarizing the dielectric. That means opposite charges moving in opposite directions in the molecules of the dielectric, removing them from their equilibrium positions and increasing their energy. So not all the work done by electric field of the capacitor transforms into kinetic energy of the dielectric, even in lack of friction. The work done on the molecules and dipoles is lost, as it transforms to heat and radiation.

ehild

4. Jul 26, 2011

### pc2-brazil

When it says that "The capacitor + blade system has a constant energy of 1055 pJ", does it mean that the total energy is initially the energy in the capacitor's electric field, and the blade has initially no energy because it is at rest?
So, the blade is pushed by the electric field and its maximum kinetic energy is 893 pJ and it occurs at the point when it fills entirely the space between the plates. On the other hand, if the blade is inserted into the capacitor by an external agent, this agent will have to do a negative total work (equal to -893 pJ) to insert the blade at constant velocity, by exerting in the blade a force of equal magnitude and opposite direction than the force that the capacitor is exerting to push the blade. Is this right?