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I have two plates, one on top of the other, that have a charge densities +s1 of the top of the top plate, -s2 on the bottom of the top plate, s2 on the top of the bottom plate, and -s1 on the bottom of the bottom plate (s1 and s2 are both positive numbers). I have to find the electric field on top of the plates, inbetween, and below the plates. Using gauss's law I drew a cylinder through the top plate and found the electric field to be s1/e (e=permittivity of free space). On the bottom by symmetry the electric field would be -s1/e. Now my problem is finding the E field inbetween. The E field vector goes away from positive charge and goes toward negative charges. So If i make a cylinder for that goes through the top plate and find the amount of E field going through the bottom part of the cylinder I have E=-s2/e. Now for the bottom plate the E filed points away from the top part of the bottom plate so by using a cylinder and Gauss's law again I have E=s2/e. Thus the E field inbetween should be -s2/e + s2/e=0. But I don't see how this is the case since the E field vector from the bottom plate is in the same direction as the E field vector of the top plate since the bottom is positively charged and the top is negatively charged. Shouldn't I get E=2s2/e ?
What am I doing wrong? (I hope I didn't get you confused, but I don't know how to do latex.)
What am I doing wrong? (I hope I didn't get you confused, but I don't know how to do latex.)