Step 1: Calculate the total electrical potential energy stored in the capacitor
The formula for the electrical potential energy (\(U\)) stored in a capacitor is given by:
\[ U = \frac{1}{2} QV \]
where:
- \( Q \) is the charge stored on the capacitor (\(3.85 \, \mu\text{C} = 3.85 \times 10^{-6} \, \text{C}\))
- \( V \) is the potential difference across the plates (\(148 \, \text{V}\))
Plugging in the values:
\[ U = \frac{1}{2} \times 3.85 \times 10^{-6} \, \text{C} \times 148 \, \text{V} \]
\[ U = \frac{1}{2} \times 569.8 \times 10^{-6} \, \text{J} \]
\[ U = 284.9 \times 10^{-6} \, \text{J} \]
\[ U = 2.849 \times 10^{-4} \, \text{J} \]
Step 2: Determine the number of excess electrons on the negatively charged plate
The number of excess electrons (\(n\)) can be found using the total charge (\(Q\)) and the charge of one electron (\(e = 1.60 \times 10^{-19} \, \text{C}\)):
\[ n = \frac{Q}{e} \]
\[ n = \frac{3.85 \times 10^{-6} \, \text{C}}{1.60 \times 10^{-19} \, \text{C/electron}} \]
\[ n = 2.40625 \times 10^{13} \, \text{electrons} \]
Step 3: Calculate the energy per excess electron
The energy per excess electron (\(U_e\)) is the total energy divided by the number of excess electrons:
\[ U_e = \frac{U}{n} \]
\[ U_e = \frac{2.849 \times 10^{-4} \, \text{J}}{2.40625 \times 10^{13} \, \text{electrons}} \]
\[ U_e = 1.184 \times 10^{-17} \, \text{J/electron} \]
Final Answer
The electrical potential energy stored per excess electron on the capacitor's negatively charged plate is:
\[ 1.18 \times 10^{-17} \, \text{J/electron} \]
Thus, the electrical potential energy stored per excess electron is \(1.18 \times 10^{-17} \, \text{J}\) to two decimal places in scientific notation.
