When a charge of amount Q is given to an isolated metal plate X of surface area A- its surface charge density becomes - 1- When an isolated identical plate Y is brought close to X- the surface charge density on X becomes -2- When y is earthed- the surface charge density becomes -3-

The correct options are A σ_1=Q2A C σ_1=σ_2 D σ_3=QA #10; #10; #10; #10; #10; #10; #10; #10; #10; #10; #10; #10; #10 ...

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Byju's Answer

Standard XII

Physics

Capacitance of Parallel Plate Capacitor

When a charge...

Question

When a charge of amount Q is given to an isolated metal plate X of surface area A, its surface charge density becomes $σ_{1}$ . When an isolated identical plate Y is brought close to X, the surface charge density on X becomes $σ_{2}$ . When y is earthed, the surface charge density becomes $σ_{3}$ .

σ_{1} = \frac{Q}{A}

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σ_{1} = \frac{Q}{2 A}

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σ_{1} = σ_{2}

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σ_{3} = \frac{Q}{A}

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Solution

The correct options are
A $σ_{1} = \frac{Q}{2 A}$
C $σ_{1} = σ_{2}$
D $σ_{3} = \frac{Q}{A}$

As the plate X is isolated so the charge remains constant on the both surface of X.

As charge Q is distribute into two surfaces of X so the charge density is $σ_{1} = \frac{Q}{A + A} = \frac{Q}{2 A}$

When another isolated plate Y is placed closed to X , the charge density of X will remain same. i.e, $σ_{2} = σ_{1}$

When Y is earthed, the system acts like a parallel plate capacitor. The charge will from near surface of X to Y. The charge will remain only on the one surface.

now charge density is $σ_{3} = \frac{Q}{A}$

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Table-1 Table-2

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When a charge of amount Q is given to an isolated metal plate X of surface area A, its surface charge density becomes σ1. When an isolated identical plate Y is brought close to X, the surface charge density on X becomes σ2. When y is earthed, the surface charge density becomes σ3.