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):(adsbygoogle = window.adsbygoogle || []).push({});

"A parallel plate capacitor, whose capacitance C_{0}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 (κ_{e}= 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 [itex]U_i = \frac{1}{2}C_0V^2[/itex] = 1055 pJ.

The final energy is [itex]U_f = \frac{q^2}{2C} = \frac{q^2}{2\kappa_eC_0} = \frac{U_i}{\kappa_e}[/itex] = 162 pJ.

The final energy is less than the initial energy by a factor of 1/κ_{e}.

The "missing" energy is due to the fact that the capacitor exerted a force on the blade, doing work given by:

[itex]W = U_i - U_f[/itex] = 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 movementparallelto the plates?

Thank you in advance.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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

**Physics Forums | Science Articles, Homework Help, Discussion**