A parallel-plate capacitor is charged to an electric potential of 345 V
 by moving 3.90×1016 electrons from one plate to the other. How much work is done in charging the capacitor?

To find the work done in charging the capacitor, we use the concept that moving charge against an electric potential difference requires work. For a parallel-plate capacitor, the work \( W \) required to move charge \( Q \) across a potential difference \( V \) is given by:

\[
W = Q \times V
\]

### Step 1: Determine the charge \( Q \)
The problem states that \( 3.90 \times 10^{16} \) electrons are moved. The elementary charge (the charge of one electron) is \( e = 1.6 \times 10^{-19} \, \text{C} \). Thus, the total charge \( Q \) moved is:

\[
Q = (3.90 \times 10^{16}) \times (1.6 \times 10^{-19}) = 6.24 \times 10^{-3} \, \text{C}
\]

### Step 2: Calculate the work \( W \)
Now, using \( V = 345 \, \text{V} \):

\[
W = Q \times V = (6.24 \times 10^{-3}) \times 345
\]

\[
W = 2.15 \, \text{J}
\]

### Answer
The work done in charging the capacitor is approximately **2.15 joules**.

Would you like further explanation on any step, or have more questions?

---

1. What is the relationship between work and electric potential in capacitors?
2. How does the number of electrons affect the work required?
3. Why is the elementary charge important in calculating charge?
4. What other factors can affect the work needed in charging a capacitor?
5. How would the work change if the potential difference was doubled?

**Tip:** For capacitors, remember that work done relates directly to the electric potential and charge transferred.

A parallel-plate capacitor is charged to an electric potential of 345 V by moving 3.90×10^16 electrons from one plate to the other. How much work is done in charging the capacitor?

Learn how to calculate the work done in charging a capacitor with a potential difference of 345 V by moving 3.90×10^16 electrons between plates. The solution uses key electrostatic formulas including W = Q × V and the elementary charge of an electron.

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