Question
There identical metal plates with large surface areas are kept parallel to each other as shown in figure (30-E8). The leftmost plate is given a charge Q, the rightmost a charge -2 Q and the middle one remains neutral. Find the charge appearing on the outer surface of the rightmost plate.
There identical metal plates with large surface areas are kept parallel to each other as shown in figure (30-E8). The leftmost plate is given a charge Q, the rightmost a charge -2 Q and the middle one remains neutral. Find the charge appearing on the outer surface of the rightmost plate.
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Solution
Consider the gaussian surface the induced charge be as shown in fig.
The nef field at p due to all the charge is zero
−2Q+q2A∈0 (left) +q2A∈0(right)+q−q2A∈0(right)=0
−2Q+q−Q+q=0
q=32 Q
charge on the right side of right most plate
=−2Q+q=−2 Q+32 Q
=−Q2
Consider the gaussian surface the induced charge be as shown in fig.
The nef field at p due to all the charge is zero
−2Q+q2A∈0 (left) +q2A∈0(right)+q−q2A∈0(right)=0
−2Q+q−Q+q=0
q=32 Q
charge on the right side of right most plate
=−2Q+q=−2 Q+32 Q
=−Q2
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