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Figure shows three large metallic plates...

Figure shows three large metallic plates with chrges `-Q, 3Q` and `Q` respectively. Determine the final charges on all the surfaces.

Text Solution

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We assume that charge on surface `2` is x. Following conservation of charge, we see that surfaces `1` has charge `(-Q-x)`. The electric field inside the metal plate is zero so field at P is zero.

Resultant field at O : `E_(p)=0 rArr (-Q-x)/(2A epsilon_(0))=(x+3Q+Q)/(2A epsilon_(0))rArr -Q-x=x+4QrArr x=(-5Q)/2`
Note : We see that charges on the facing surfaces of the plates are of equal magnitude and opposite sign. This can be general proved by gauss theorem also. Remember this it is important result.
Thus the final charge distribution on all the surfaces is :
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Knowledge Check

  • Three concentric metallic spherical shells of radii R, 2R, 3R, are given charges Q_1 , Q_2 , Q_3 , respectively. It is found that the surface charge denisties on the outer surfaces of the shells are equal. Then, the ratio of the charges given to the shells, Q_1:Q_2:Q_3 , is

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