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Q.

The figure shows three infinite non-conducting plates of charge perpendicular to the plane of the paper with charge per unit area $+ σ, + 2 σ and - σ$ . Find the ratio of the net electric field at that point A to that at point B.

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a

$\frac{σ}{2 ε_{0}}$

b

$\frac{3 σ}{2 ε_{0}} \hat{j}$

c

$\frac{2 σ}{3 ε_{0}} \hat{j}$

d

0

answer is D.

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Detailed Solution

The electric field intensity at point A due to plate x, y and z

$\begin{array}{l} E_{A} = E_{x} + E_{y} + E_{z} \\ \frac{σ}{2 \in_{0}} - \frac{2 σ}{2 \in_{0}} + \frac{σ}{2 \in_{0}} \\ E_{A} = 0 ................. (1) \\ At point B \\ E_{B} = \frac{σ}{2 \in_{0}} + \frac{2 σ}{2 \in_{0}} + \frac{σ}{2 \in_{0}} \\ E_{B} = \frac{4 σ}{2 \in_{0}} . ............. (2) \\ From equation (1) & (2) \\ \frac{E_{A}}{E_{B}} = 0 \end{array}$

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