# Gauss's Law / Dielectric Boundary

Consider a charged capacitor with two different dielectric materials, as shown. The electric fields point from the positive plate to the negative plate. Determine the relationship between the electric fields $E_1$ and $E_2$.

Draw a Gaussian surface around the dielectric boundary as shown, and apply Gauss's law to the closed surface.

$\int \int \epsilon \vec{E} \cdot \vec{dS} = Q$

In the above equation, $Q$ is the enclosed free charge at the dielectric interface. In the ordinary "text book" case, $Q = 0$. Integrating over the top and bottom surfaces results in (assuming the top and bottom surfaces have area $A$):

$\epsilon_1 E_1 A - \epsilon_2 E_2 A = 0 \\ \epsilon_1 E_1 = \epsilon_2 E_2$

Note by Steven Chase
8 months, 1 week ago

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@Talulah Riley I will be traveling most of the day today, so this might be the last thing I post

- 8 months, 1 week ago

@Steven Chase where you are travelling? For your work or chilling your life??

- 8 months, 1 week ago

@Steven Chase Thanks for the note.

- 8 months, 1 week ago