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Question

An isolated large conducting plate having area A and total charge Q is placed in a uniform electric field →E as shown in the figure. If q1 and q2 are the charges appearing on the two sides of the plate, then



A
q1=Q2EAε0, q2=Q2+EAε0
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B
q1=Q2+EAε0 , q2=Q2EAε0
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C
q1=Q3, q2=Q2EAε0
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D
None of the above
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Solution

The correct option is A q1=Q2EAε0, q2=Q2+EAε0
Given,
Net charge on the plate=Q
Area of the plate=A

Let us consider a point P inside the plate as shown in figure.


As we know that, electric field at point P inside the conductor is zero. So,
Enet=0

Electric field at point P due to charge q1 is q12Aεo as shown in figure.

Similary,
Electric field at point P due to charge q2 is q22Aεo as shown in figure.

Thus, net electric field at point P,

Enet=q12Aεo+Eq22Aϵ0

Since, Enet=0, so we have

q12Aεo+Eq22Aϵ0=0.......(1)

Also, from conservation of charge,
q1+q2=Q.......(2)

From (1) and (2), we have

q12Aεo+EQq12Aϵ0=0

q12Aεo+EQ2Aϵ0+q12Aϵ0=0

q1Aεo=Q2AεoE

q1=Q2EAεo

From equation (2),
q2=Q2+EAε0

Hence option (a) is the correct answer.

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