Question

Having trouble setting the formula up for this question, how do I get the Area if the width is not given?

A capacitor is constructed from two square, metallic plates of sides ! and separation d. Charges +Q and -Q are placed on the plates, and the power supply is then removed. A material of dielectric constant K is inserted a distance x into the capacitor as shown in the figure below. Assume d is much smaller than x. Suggestion: The system can be considered as two capacitors connected in parallel. (Use the following as necessary: Eo, k, l, Q, d, and x.) + + + x d - - - - - - (a) Find the equivalent capacitance of the device. Cea = (b) Calculate the energy stored in the capacitor. (c) Find the direction and magnitude of the force exerted by the plates on the dielectric. magnitude direction Direction

Answer 1

Given that the length of each side of the conducting plate is L Separation between the two plates is D and dimension of the di electric slab is LxLxD. (a) thegiven capacitor acts as two capacitors that are in parallel. Here one plate area (1 - x) and air between the plates and the other with area Lx and a dielectric with costant fills between the plates. The capacitance of a parallel plate capacitor is, For air filled capacitor, G=!(1-x) For di electric field capacitor, C = Home The two capacitors are in parallel, the resultant capacitance is, C=C+02 1(1-x) & kdxe d = (2+(x=137) The energy stored in the capacitor is, v=_cva - * – 1) x+) The capacitor when dielectric slab inserted an additional distance dx is, Co - (-da+kda) - Elda (k-1) Now the energy stored is dU = (Ca)p ja edat (k-1)]

The relation between the change in potential energy and force applied is, dU=- Fdx - Fdx=- (k-1) &V Ldx we determine that the plates plus slab are not considered to be an isolated system whenever the plates are connected to the battery. we also conclude that in addition to the work that is done on the slab by the charges on one plate energy also transferred between the paltes and battery, from the above equation force is, F -- EVA (-1) la bele 2d la pista de este bandit Here, k>1, the force points left, in a direction to push the di electric out bf the capacitor.