An electron enters between two horizontal plates separated by `2 mm` and having a potential difference of `1000V`. The force on electron is

Options

A. `8 xx 10^(-12) N`
B. `8 xx 10^(-14) N`
C. `8 xx 10^(-9) N`
D. `8 xx 10^(14) N`

Explanation

To solve the problem of finding the force on an electron entering between two horizontal plates, we can follow these steps:

### Step 1: Identify the given values
- Potential difference (V) = 1000 V
- Separation between the plates (d) = 2 mm = 2 × 10^(-3) m
- Charge of an electron (q) = -1.6 × 10^(-19) C

### Step 2: Calculate the electric field (E)
The electric field (E) between two parallel plates is given by the formula:
\[ E = \frac{V}{d} \]
Substituting the known values:
\[ E = \frac{1000 \, \text{V}}{2 \times 10^{-3} \, \text{m}} \]
\[ E = \frac{1000}{0.002} \]
\[ E = 500000 \, \text{V/m} \]
\[ E = 5 \times 10^5 \, \text{V/m} \]

### Step 3: Calculate the force (F) on the electron
The force (F) on a charge in an electric field is given by:
\[ F = qE \]
Substituting the values:
\[ F = (-1.6 \times 10^{-19} \, \text{C})(5 \times 10^5 \, \text{V/m}) \]
\[ F = -8 \times 10^{-14} \, \text{N} \]

### Step 4: Interpret the result
The negative sign indicates that the force is acting in the direction opposite to the electric field (since the electron has a negative charge). However, the magnitude of the force is:
\[ F = 8 \times 10^{-14} \, \text{N} \]

### Final Answer
The force on the electron is \( 8 \times 10^{-14} \, \text{N} \).

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