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Two points P and Q are maintained at potentials of $10$V and $-4$V respectively. The work done in moving $100$ electrons from P to Q is proportional to
(A) $2.24\times {{10}^{-16}}$J
(B) $-9.6\times {{10}^{-17}}$J
(C) $-2.24\times {{10}^{-16}}$J
(D) $9.6\times {{10}^{-17}}$J

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Last updated date: 20th Jun 2024
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Answer
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Hint: The work done to move a charge or group of charge from one point P to another point Q is proportional to the amount of charge moved (magnitude of charge) and it is proportional to the potential difference between the two points P and Q.

Complete answer:
According to the question, let us consider two points P and Q, they are maintained at potentials of $10$V and $-4$V respectively, as shown in the figure below.
seo images

The potential difference between the two points P and Q is given by,
${{V}_{d}}=(-4)-10=-14$V ….(i)
We have to move $100$ electrons from P to Q, so the charge equivalent to $100$ electrons will be 100 multiplied by c the charge of one electron, we get,
$q=100\times (-1.6\times {{10}^{-19}})=-1.6\times {{10}^{-17}}$C ….(ii)
We know that the work done to move a charge from one point P to another point Q depends on the magnitude of charge and the potential difference between the two points P and Q.
Work done is given by,
$W=q\times {{V}_{d}}$ ….(iii)
Now, putting the values of potential difference ${{V}_{d}}$ from equation (i) and charge q from equation (ii), in the above formula, we get work done as,
$W=(-1.6\times {{10}^{-17}})\times (-14)=2.24\times {{10}^{-16}}$J
Hence, $2.24\times {{10}^{-16}}$J of work is done to move $100$ electrons from point P to point Q.

Thus, the correct answer is option (A).

Additional Information:
S.I. unit of charge is Coulomb, S.I. unit of work done is Joule and S.I. unit of force is Newton.

Note:
The value of charge of one electron is $-1.6\times {{10}^{-19}}$C and should be remembered to solve questions. Electric potential, the work done to move a point charge from one point to another is the electric potential energy per unit charge and it is a scalar quantity.