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teme92
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Homework Statement
(a) Calculate the Electric displacement of parallel plate capacitor of with a thickness d (in z), and length L (in x), and a width W (in y). Within the capacitor is a dielectric oil with a dielectric constant –εr , and the charge on the plates is ± q.
(b) Using the definition of Electric displacement, what is the Electric field within the capacitor?
(c) Calculate the capacitance? (
d) If the capacitor is turned sideways so that the width W is vertical, while the length L and thickness d are horizontal, how much oil will remain within the capacitor? (provide either a volume or a length) Assume that the density of the dielectric oil is ρ . (Warning: your final solution may not be closed form and if so, need not be fully solved)
Homework Equations
The Attempt at a Solution
(a) Used Gauss' Law:
[itex]\int D{\cdot}da = Q[/itex] where [itex]\int D{\cdot}da = 2DA[/itex].
Therefore: [itex]D = \frac{Q}{2A} = \frac{\sigma}{2}\hat{z}[/itex]
(b) D is proportional to electric field as dielectric material is linear:
[itex]E = -\frac{\sigma}{2\epsilon_r}[/itex]
(c) Used the formula:
[itex]C = \epsilon_r\epsilon_0\frac{A}{d}[/itex]
(d) Have no idea how to begin this part even. Any help in the right direction would be greatly appreciated.