Physics 1251 HW 3 #10

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I was reviewing gaussian surfaces for the midterm and was trying to do this problem.  My process was as follows.  It says you have a square plate of copper so I drew a cylinder going through the plate. This would give you two areas on both sides that have flux going through them. Therefore my equation was

2EA=((sigma)(A))/(epselon naut). This gave an answer that was half of the correct answer. Therefore it is obvious that the equation should be just EA=((sigma)(A))/(epselon naut), without the 2. But I dont understand how this could be correct since you have a thin plate of charge, not a thick conducting wall. An explanation on this problem would be great.

asked Oct 8, 2014 in General

The conducting plate is thin, but it still has two surfaces (Top and Botttom). In between these, there must be a net electric field of zero, because copper is a conductor. To find $\sigma$ you will need to look at the electric field in the region INSIDE the conductor where the external electric field and the E-field induced in the copper will cancel each other out. This will require adding the components of the electric field from both the top and bottom surfaces, giving you the "2" you were looking for.