Dumb electromagnetics question (dielectrics)

[Dynam0]

Re: Dumb electromagnetics question (dielectrics)

Yes! I think that makes sense. Capacitance is the ability to store charge so the value of capacitance in each chunk is additive when representing the whole system.

[MarioNintendo]

Re: Dumb electromagnetics question (dielectrics)

I agree, Dynam0, that's been bugging me too.

BUT:

Instead of taking a weighted average of the capacitances (since the weighted averaging was, I guess, taken into account via the area partitioning of the initial two equations), if you just add them together lol:

k = .01 * (1.7708 * 10^(-12)+1.15102 * 10^(-11)) / (.05*.05 * 8.854 * 10^(-12) ) = 6

So maybe it works that way instead and it really is that simple, haha

Tried to follow, but I get stumped here... What are these numbers?

also, damn that picture was unexpected, lol! You guys work in a professional manner, to say the least.

Uhh... :/

In other words, we want the algebraic answer and the numerical answer for the capacitance of this dielectric capacitor.

[Reincarnate]

Re: Dumb electromagnetics question (dielectrics)

Corrected version of my earlier post:

C = k * epsilon_0 * A / d

where
C = capacitance (farad)
A = area (m^2)
d = distance (m)
k = dielectic constant
epsilon_0 = 8.854 * 10^(-12) F/m

For the k1 chunk
C_1 = 4 * 8.854 * 10^(-12) F/m * (.05*.01) m^2 / (.01 m) = 1.7708 * 10^(-12) F

For the k2 chunk
C_2 = 6.5 * 8.854 * 10^(-12) F/m * (.05*.04) m^2 / (.01 m) = 1.15102 * 10^(-11) F

Add the capacitances together to get the value for the whole system:

C_system = C_1 + C_2 = 1.7708 * 10^(-12) F + 1.15102 * 10^(-11) F = 1.3281 * 10^(-11) F

Now we solve for our new k from the original equation (rearranged): k = d*C / (A * epsilon_0)

k_system = .01 m * (1.3281 * 10^(-11) F) / ((.05*.05) m^2 * 8.854 * 10^(-12) F/m) = 6

So in the end, it comes down to the following:

k_system = (1/5)*(4) + (4/5)*(6.5) = 6



Algebraic answer:

k_system = (A_1 / (A_1 + A_2)) * k_1 + (A_2 / (A_1 + A_2)) * k_2

Where A_1 is the area of the plate corresponding to the k_1 stuff and A_2 is the area of the plate corresponding to the k_2 stuff

[MarioNintendo]

Re: Dumb electromagnetics question (dielectrics)

Thanks a bunch you two. I mean it!