Two points P and Q are maintained at the potentials of 10V and -4V, respectively. The work done in moving 100 electrons from P to Q is:

Options

A. `-19 xx 10^(-17) J`
B. `9.60 xx 10^(-17) J`
C. `-2.24 xx 10^(-16) J`
D. `2.24 xx 10^(-16) J`

Answer

To find the work done in moving 100 electrons from point P to point Q, we can follow these steps:

### Step 1: Identify the potentials at points P and Q
- The potential at point P (V_P) is 10 V.
- The potential at point Q (V_Q) is -4 V.

### Step 2: Calculate the potential difference (ΔV)
- The potential difference (ΔV) when moving from point P to point Q is given by:
\[ ΔV = V_P - V_Q = 10 V - (-4 V) = 10 V + 4 V = 14 V \]

### Step 3: Calculate the total charge of 100 electrons
- The charge of a single electron (e) is approximately \(1.6 \times 10^{-19}\) coulombs.
- Therefore, the total charge (Q) for 100 electrons is:
\[ Q = 100 \times e = 100 \times 1.6 \times 10^{-19} \text{ C} = 1.6 \times 10^{-17} \text{ C} \]

### Step 4: Calculate the work done (W)
- The work done (W) in moving charge through a potential difference is given by:
\[ W = Q \times ΔV \]
- Substituting the values we have:
\[ W = (1.6 \times 10^{-17} \text{ C}) \times (14 \text{ V}) = 2.24 \times 10^{-16} \text{ J} \]

### Conclusion
- The work done in moving 100 electrons from point P to point Q is:
\[ W = 2.24 \times 10^{-16} \text{ J} \]

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