Three identical, parallel conducting plates A, B and C are placed as shown. Switches $S_1$ and $S_2$ are open, and can connect A and C to earth when closed. +Q charge is given to B, then:
(a) if $S_1$ is closed with $S_2$ open, a charge of amount Q will pass through $S_1$ (b) if $S_2$ is closed with $S_1$ open, a charge of amount Q will pass through $S_2$ (c) if $S_1$ and $S_2$ are closed together, a charge of amount Q/3 will pass through $S_1$ and a charge of amount $2Q/3$ will pass through $S_2$. (d) All of the above.
My first step:
@JohnRennie: Could you please tell how to proceed from this? I understand earthing a conductor makes its potential equal to that of earth close to 0 volts. But I think we need to determine the potentials of the individual plates for which I don't know any method.
The charge on B has to add to $+Q$ and the way you have drawn it the charges add up to zero i.e. you've drawn $+Q/2$ on one face and $-Q/2$ on the other.
One of the ways examiners torture students is by asking them to calculate charge distributions and potentials for systems of charged parallel plates like this:
the ellipsis is meant to indicate any number of additional plates could be inserted where I've placed the ellipsis. The plates are ass...
And we know the charge on the outer surface has to be zero because we have one plate (A) earthed. That means the inner face of C must also have zero charge.
And that means the charge on the right face of plate B must also be zero. OK so far?
Ok sir. $-Q$ from the ground to the plate is same as $+Q$ from the plate to the ground. I usually like to use positron picture rather than the electron picture as I like to be positive :-)
That's it. I got the same result as of your method of using electric field density.
The two capacitors AB and BC are in parallel and the potential difference across the terminals is equal. Using this I found the charge on individual plates.
One of the ways examiners torture students is by asking them to calculate charge distributions and potentials for systems of charged parallel plates like this:
the ellipsis is meant to indicate any number of additional plates could be inserted where I've placed the ellipsis. The plates are ass...
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