To calculate the work done when moving an electron from the positive plate to the negative plate in an electric field, you can use the formula:
\[ W = q \cdot V \]
Where:
- \( W \) is the work done,
- \( q \) is the charge of the electron, and
- \( V \) is the potential difference between the plates.
First, we need to find the potential difference \( V \). The potential difference can be related to the electric field \( E \) and the distance \( d \) between the plates using the formula:
\[ V = E \cdot d \]
Given:
- \( E = 700 , \text{N/C} \)
- \( d = 3.0 , \text{cm} = 0.03 , \text{m} \)
Calculating \( V \):
\[ V = 700 , \text{N/C} \times 0.03 , \text{m} = 21 , \text{V} \]
Next, we can find the work done when moving an electron (with charge \( q = 1.6 \times 10^{-19} , \text{C} \)):
\[ W = q \cdot V = (1.6 \times 10^{-19} , \text{C}) \times (21 , \text{V}) \]
Calculating \( W \):
\[ W = 1.6 \times 10^{-19} \times 21 = 3.36 \times 10^{-18} , \text{J} \]
Thus, the work done when the electron is moved from the positive plate to the negative plate is:
\[ \boxed{3.36 \times 10^{-18} , \text{J}} \]