Capacitance Formula for Parallel Plate Capacitor with Dielectric Material?

[yjk91]

Homework Statement

A capacitor has parallel plates, with half of the space between the plates filled with a dielectric material of constant κ and the other half filled with air as shown in the figure. Assume that the plates are square, with sides of length L, and that the separation between the plates is s. Determine the capacitance as a function of L. (Use any variable or symbol stated above along with the following as necessary: ε0.)

http://www.webassign.net/bauerphys1/24-p-050.gif

The Attempt at a Solution

From the figure, there are two capasitors in parallel circuit.
C = C1 + C2
= εo * A/d + εo * A/d
= εo * 0.5L*L/s + Kεo * 0.5L * L/s
= (εo * 0.5L^2/s)(1 + κ )
--> C = (εo*L^2/2s)(1 + κ )


mm where did i got wrong?

 

[berkeman]

Homework Statement

A capacitor has parallel plates, with half of the space between the plates filled with a dielectric material of constant κ and the other half filled with air as shown in the figure. Assume that the plates are square, with sides of length L, and that the separation between the plates is s. Determine the capacitance as a function of L. (Use any variable or symbol stated above along with the following as necessary: ε0.)

http://www.webassign.net/bauerphys1/24-p-050.gif

The Attempt at a Solution

From the figure, there are two capasitors in parallel circuit.
C = C1 + C2
= εo * A/d + εo * A/d
= εo * 0.5L*L/s + Kεo * 0.5L * L/s
= (εo * 0.5L^2/s)(1 + κ )
--> C = (εo*L^2/2s)(1 + κ )


mm where did i got wrong?

The answer looks correct to me. There is a typo in your 2nd equation, where you should either have the terms be just ε, or the 2nd term should be Kεo, but you correct that in the 3rd equation, and the rest looks okay. It gives the correct answer when K=1, for example.