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. (a) `9.60xx10^-17J`
B. (b) `-2.24xx10^-16J`
C. (c) `2.24xx10^-16J`
D. (d) `-9.60xx10^-17J`

Explanation

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

### Step 1: Understand the potentials
- Point P has a potential of \( V_P = 10 \, \text{V} \).
- Point Q has a potential of \( V_Q = -4 \, \text{V} \).

### Step 2: Calculate the potential difference
The potential difference \( V \) between points P and Q is given by:
\[ V = V_Q - V_P \]
Substituting the values:
\[ V = -4 \, \text{V} - 10 \, \text{V} = -14 \, \text{V} \]

### Step 3: Calculate the charge of 100 electrons
The charge of a single electron is approximately \( e = 1.6 \times 10^{-19} \, \text{C} \). Therefore, the total charge \( Q \) of 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
The work done \( W \) in moving the charge \( Q \) through a potential difference \( V \) is given by:
\[ W = Q \times V \]
Substituting the values we calculated:
\[ W = (1.6 \times 10^{-17} \, \text{C}) \times (-14 \, \text{V}) = -2.24 \times 10^{-16} \, \text{J} \]

### Final Answer
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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