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Question

A uniform electric field exists between two charged plates as shown in the fig. What should be the work done in moving a charge q along the closed reactangular path ABCDA

Solution
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Work done in an electric field is independent of the path and depends only on the initial and final positions.
Here initial and final points are coincident.

$$ W=q\times (V_{final}-V_{initial} ) $$

$$W= q (VA-VA)$$

So, net work done is zero.

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