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Question: Two points P and Q are maintained at potentials of \(10\)V and \(-4\)V respectively. The work done i...

Two points P and Q are maintained at potentials of 1010V and −4-4V respectively. The work done in moving 100100 electrons from P to Q is proportional to
(A) 2.24×10−162.24\times {{10}^{-16}}J
(B) −9.6×10−17-9.6\times {{10}^{-17}}J
(C) −2.24×10−16-2.24\times {{10}^{-16}}J
(D) 9.6×10−179.6\times {{10}^{-17}}J

Explanation

Solution

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 1010V and −4-4V respectively, as shown in the figure below.

The potential difference between the two points P and Q is given by,
Vd=(−4)−10=−14{{V}_{d}}=(-4)-10=-14V ….(i)
We have to move 100100 electrons from P to Q, so the charge equivalent to 100100 electrons will be 100 multiplied by c the charge of one electron, we get,
q=100×(−1.6×10−19)=−1.6×10−17q=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×VdW=q\times {{V}_{d}} ….(iii)
Now, putting the values of potential difference Vd{{V}_{d}} from equation (i) and charge q from equation (ii), in the above formula, we get work done as,
W=(−1.6×10−17)×(−14)=2.24×10−16W=(-1.6\times {{10}^{-17}})\times (-14)=2.24\times {{10}^{-16}}J
Hence, 2.24×10−162.24\times {{10}^{-16}}J of work is done to move 100100 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 −1.6×10−19-1.6\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.