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Induced Charges

three paralle...

Question

three parallel metallic plates each of area a are kept apart and charges Q1,Q2,Q3are given to them.effect edges are negligible.calculate the charges on the two outermost surfaces of the parallel plate capacitor

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Solution

Charge on plates is shown in fig and mathematically we can write ,

$q_{1} + q_{2} = Q_{1} . . . . . (1)$
$- q_{2} + q_{3} = Q_{2} . . . . . (2)$
$q_{4} - q_{3} = Q_{3} . . . . . . . . . (3)$
Adding equation (1, (2) and(3)

$q_{1} + q_{4} = Q_{1} + Q_{2} + Q_{3}$
$q_{1} = q_{4}$
As, charge on both end is same so,
$2 q_{1} = Q_{1} + Q_{2} + Q_{3}$
$q_{1} = \frac{Q_{1} + Q_{2} + Q_{3}}{2}$

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