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Q.

Two uniformly charged large plane sheets S₁ and S₂ having charge densities $σ_{1} & σ_{2} (σ_{1} > σ_{2})$ are placed at a distance (d) parallel to each other. A charge q is moved along a line of length (a < d) at 45° with normal to S₁. Then, work done by electric field is:

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a

$\frac{(σ_{1} - σ_{2}) a}{2 \in_{0} q}$

b

$\frac{q (σ_{2} - σ_{1}) a}{\sqrt{2} \in_{0}}$

c

$\frac{q (σ_{1} - σ_{2}) a}{\sqrt{2} \in_{0}}$

d

$\frac{(σ_{1} - σ_{2})}{2 aq} \in_{0}$

answer is A.

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Detailed Solution

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$∴ Net field at q = E_{1} - E_{2} E = \frac{σ_{1} - σ_{2}}{ϵ_{0}} ∴ W = qE \times \frac{a}{\sqrt{2}} = \frac{qE (σ_{1} - σ_{2}) a}{\sqrt{2} ϵ_{0}}$

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Two uniformly charged large plane sheets S1 and S2 having charge densities σ1&σ2(σ1>σ2) are placed at a distance (d) parallel to each other. A charge q is moved along a line of length (a < d) at 45° with normal to S1. Then, work done by electric field is: