Appearance of Charge

Electricity and Magnetism Level 1

3 3 identical plates with large surface areas are kept parallel to each other as shown. The leftmost plate is given a charge Q Q , the rightmost plate is given a charge − 2 Q -2Q and the middle plate is kept neutral.

Find the charge appearing on the outer surface of the rightmost plate.

+ Q 2 \frac{+Q}{2} − Q 2 \frac{-Q}{2} − Q -Q + Q +Q 0

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1 solution

Using Gauss's Law in electrostatics, we get the following induced charge distribution:

Note that the plates have been evaluated in parts before summing the charges for each surface; first by considering the leftmost plate and then by considering the rightmost plate.

Therefore, net charge on the outer surface of the rightmost plate = − Q + Q 2 = − Q 2 = -Q + \frac{Q}{2} = \boxed{\frac{-Q}{2}}

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