Hey ... I'm trying to study for my PhD qualifying exam, and I have a bunch of questions from previous years, but no answer keys.(adsbygoogle = window.adsbygoogle || []).push({});

1. The problem statement, all variables and given/known data

A think uniformly charged rod of length L is positioned vertically above a large uncharged horizontal thick metal plate. The distance between the lower end of the rod and the metal plate is S.

If the total charge of the rod is q, find the charge density [tex]\sigma[/tex] on the upper surface of the metal plate directly below the rod. (Hint: First, consider only the rod and find the electric field due to he rod at a distance S directly below the rod.)

2. Relevant equations

3. The attempt at a solution

I found the electric field due to the rod to be

[tex]E_{rod}=\int_{S}^{S+L}{\frac{kQ}{L^2z^2}dz}[/tex]

[tex]E_{rod}=-\left.\frac{kQ}{Lz}\right|^{S+L}_{S}[/tex]

[tex]E_{rod}=\frac{kQ}{S(S+L)}[/tex]

I'm not sure where to go from here. If the plate was grounded, we could use an image charge and

[tex]\sigma=\epsilon_0E_n[/tex]; is this also the right approach for the present problem, given that we're only considering the point directly below the rod?

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# Homework Help: [PhD Qualifier] Charged rod above metal plate

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