Question

Two Points \(P\) and \(Q\) are maintained at the Potentials of \(10 \mathrm{v}\) and \(-4 \mathrm{v}\), respectively. The work done in moving 100 electrons from \(\mathrm{P}\) to \(\mathrm{Q}\) is \(\ldots \ldots \ldots\) (A) \(2.24 \times 10^{-16} \mathrm{~J}\) (B) \(-9.60 \times 10^{-17} \mathrm{~J}\) (C) \(-2.24 \times 10^{-16} \mathrm{~J}\) (D) \(9.60 \times 10^{-17} \mathrm{~J}\)

Short answer

The work done in moving 100 electrons from point P to point Q is \(-2.24 \times 10^{-16} J\).

Step-by-step solution

Identify the given values

We are given the potentials of point P as \(10V\) and point Q as \(-4V\). We are moving 100 electrons from P to Q.

Use the work done formula

The work done in moving a charge between two points in a potential field is given by the formula: \[W = q(V_B - V_A)\] Here, W: work done, q: charge being moved, \(V_A\): potential of point A (initial point), \(V_B\): potential of point B (final point). In this case, point P is the initial point and point Q is the final point. So, \(V_A = 10V\), \(V_B = -4V\), q: charge of 100 electrons.

Calculate the charge q

We know that one electron has a charge of \(1.6 \times 10^{-19} C\). So, for 100 electrons, the total charge q is: \[q = 100 \times 1.6 \times 10^{-19} C = 1.6 \times 10^{-17} C\]

Compute the work done W

Now, substitute the values we have obtained into the work done formula: \[W = (1.6 \times 10^{-17} C)(-4V - 10V)\] \[W = (1.6 \times 10^{-17} C)(-14V)\] \[W = -2.24 \times 10^{-16} J\] Therefore, the work done in moving 100 electrons from point P to point Q is \(-2.24 \times 10^{-16} J\), which is option (C).