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Infinite Line of Charge

A charge q is...

Question

A charge $q$ is moved from point $A$ to point $B$ in an uniform electric field along $4$ paths as shown below. The work done to move the charge along the paths is $W_{1}, W_{2}, W_{3} and W_{4}$ respectively. Choose the correct statement.

A

W_{4} > W_{1} > W_{2} > W_{3}

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B

W_{4} < W_{1} < W_{2} < W_{3}

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C

W_{4} = W_{1} = W_{2} = W_{3}

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D

W_{4} < W_{1} = W_{2} < W_{3}

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Solution

The correct option is C $W_{4} = W_{1} = W_{2} = W_{3}$
The electrostatic force is conservative force. So the work done to move a charge from A to B on all paths will be the same. The work done does not depend on the path, but it depends on the initial and final position only.
$\Rightarrow W_{4} = W_{1} = W_{2} = W_{3} = W_{4}$

Hence, option (c) is correct.

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