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Question
Two metallic plates X and Y, each having large surface area A(on one side), are placed parallel to each other as shown in the figure below. The plate X is given a charge q whereas the other is neutral. The surface charge density at the inner surface of the plate Y is
Two metallic plates X and Y, each having large surface area A(on one side), are placed parallel to each other as shown in the figure below. The plate X is given a charge q whereas the other is neutral. The surface charge density at the inner surface of the plate Y is
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Solution
The correct option is D q2A
Charge distribution
to ensure zero electric field inside conductor plates, it can be obtained from gauss law : the outermost faces of outermost plates get equal charges and each equal to half of the total charge.
facing surface get equal and opposite charges.
Since plate Y is neutral, net charge on it is 0.
Total charge on two plates = Q + 0 = Q
Thus, (Q2) charge will appear on outer surfaces of both plates charge distribution of plates is shown below
∴[Surface charge density of inner surface of plate Y]
= charge / surface area = −Q2A
Hence the correct option is (B).
Charge distribution
to ensure zero electric field inside conductor plates, it can be obtained from gauss law : the outermost faces of outermost plates get equal charges and each equal to half of the total charge.
facing surface get equal and opposite charges.
Since plate Y is neutral, net charge on it is 0.
Total charge on two plates = Q + 0 = Q
Thus, (Q2) charge will appear on outer surfaces of both plates charge distribution of plates is shown below
∴[Surface charge density of inner surface of plate Y]
= charge / surface area = −Q2A
Hence the correct option is (B).
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