Hello, everyone. I have a problem that I solved using Gauss's Law. However, I am unconfident in my answers, as I have very little experience with Gauss's Law.(adsbygoogle = window.adsbygoogle || []).push({});

The surfaces of two large (i.e. infinite) parallel conducting plates have charge densities as follows: [tex]\sigma_1[/tex] on the top of the top plate; [tex]-\sigma_2[/tex] on the bottom of the top plate; [tex]\sigma_2[/tex] on the top of the bottom plate; [tex]-\sigma_1[/tex] on the bottom of the bottom plate; [tex]\sigma_1 > \sigma_2[/tex]. Use Gauss's law and symmetry to calculate the electric field below, between, and above the plates.Here's how I did it:

I made a gaussian surface - a cylinder that cut through both of the plates with radius [tex]r[/tex] - in order to find the electric field above and below the plates. Then, I used Gauss's law:

[tex]\oint \vec{E}\cdot \,d\vec{A} = E\oint \,dA = \frac{q_{inside}}{\epsilon_0}[/tex].

This is the part that I doubt myself:

[tex]E(\pi r^2 + \pi r^2) = \frac{\pi r^2(\sigma_1 - \sigma_2 + \sigma_2 - \sigma_1)}{\epsilon_0} = 0[/tex]

So I concluded that below and above the plates the electric field was zero. But this did not make sense to me. Are my calculations correct? Did I put the gaussian surface in the correct place to find the electric field above and below the plates?

For between the plates, I made two different gaussian surfaces - one for each plate - that had one face in one plate and the other face in the space between the plates, such that the inside charge included both [tex]\sigma_1[/tex] and [tex]\sigma_2[/tex]. But is this the correct gaussian surface, or am I supposed to make surfaces such that the [tex]\sigma_1[/tex]'s are left out? This is very confusing!

I continued, and eventually calculated that the electric field in between the plates is [tex]-\frac{2\sigma_2 - 2\sigma_1}{\epsilon_0}[/tex], which means that's it's going downward. Is this correct?

Thank you for your help!

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# Homework Help: Gauss's Law

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