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Offline Centres

$X and Y$ 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 $A, B, C$ are as shown in the figure.

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The field at $B$ is $\frac{Q}{2 ϵ_{0} A}$

The field at $B$ is $\frac{Q}{ϵ_{0} A}$

The fields at $A, B, C$ are of the same magnitude.

The fields at $A and C$ are of the same magnitude but in opposite direction.

answer is A, C, D.

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Detailed Solution

$q_{1} = q_{4} = \frac{q_{total}}{2} = \frac{Q}{2}$

$q_{2} = Q - q_{1} = \frac{Q}{2}$

$q_{3} = - q_{2} = \frac{- Q}{2}$

$E_{A} = E_{1} + E_{4}$ (towards left)

$= \frac{Q}{4 A ε_{0}} + \frac{Q}{4 A ε_{0}} = \frac{Q}{2 A ε_{0}}$

$E_{C} = - E_{A} = \frac{Q}{2 A ε_{0}}$ (towards right)

$E_{B} = E_{2} + E_{3}$ (towards right)

$= \frac{Q}{4 A ε_{0}} + \frac{Q}{4 A ε_{0}} = \frac{Q}{2 A ε_{0}}$

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