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# X and Y are large,parallel conducting plates close to each other. Each face has an area A. X is given a charge Q. Y is without any charge. Points A, B and C are as shown in the figure then:the field at B is Q2ε0Athe field at B is Qε0Athe field at A, B and C are of the same magnitudethe fields at A and C are of the same magnitude, but in opposite directions

A
the field at A, B and C are of the same magnitude
B
the fields at A and C are of the same magnitude, but in opposite directions
C
the field at B is Q2ε0A
D
the field at B is Qε0A
Solution
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#### Charge on plate X is Q1=Q and charge on plate Y is Q2=0Charges on plate surfaces 1 and 4 are q1=q4=Q1+Q22=Q2Charge on surface 2 is q2=Q1−Q22=Q2and charge on surface 3 is q3=−q2=−Q2The field at A is EA=E1+E4=(Q/2)2Aϵ0+(Q/2)2Aϵ0=Q2Aϵ0As both 1 and 4 surfaces have same positive charge so fields at A and C are directed away from the surfaces and have equal magnitude.so are equal in magnitude but opposite in direction.Thus, EA=Q2Aϵ0 (toward left) and EC=Q2Aϵ0 (toward right)Now EB=E2+E3=Q/22Aϵ0+Q/22Aϵ0=Q2Aϵ0 (toward right) as filled is directed from positive to negative charge.

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