To find the charge on each electrode of the parallel-plate capacitor, we can use the relationship between the electric field $E$, the charge $Q$, the area $A$ of the plates, and the permittivity of free space $\varepsilon_0$:

$E = \frac{Q}{A \cdot \varepsilon_0}$

Where:

• $E$ is the electric field strength (1.0 × 10^6 N/C).
• $A$ is the area of one of the electrodes.
• $\varepsilon_0$ is the permittivity of free space, approximately $8.85 \times 10^{-12} \, \text{F/m}$.

First, we need to calculate the area $A$ of one electrode, which is circular:

$A = \pi r^2$

The radius $r$ can be found from the diameter:

$r = \frac{6.0 \, \text{cm}}{2} = 3.0 \, \text{cm} = 0.03 \, \text{m}$

Now we calculate the area:

$A = \pi (0.03 \, \text{m})^2 \approx 2.827 \times 10^{-3} \, \text{m}^2$

Now we can rearrange the equation for charge $Q$:

$Q = E \cdot A \cdot \varepsilon_0$

Substituting the known values:

$Q = (1.0 \times 10^6 \, \text{N/C}) \cdot (2.827 \times 10^{-3} \, \text{m}^2) \cdot (8.85 \times 10^{-12} \, \text{F/m})$

Calculating $Q$:

$Q \approx (1.0 \times 10^6) \cdot (2.827 \times 10^{-3}) \cdot (8.85 \times 10^{-12}) \approx 2.5 \times 10^{-18} \, \text{C}$

Now converting this charge into nanocoulombs (nC):

$Q \approx 2.5 \times 10^{-18} \, \text{C} \times 10^{9} \, \text{nC/C} \approx 2.5 \times 10^{-9} \, \text{nC} \approx 2.5 \, \text{nC}$

Thus, the charge on each electrode is approximately 2.5 nC.

If you have any questions or need further details, feel free to ask! Here are some related questions you might consider:

1. How does the capacitance change if the distance between the plates is increased?
2. What factors influence the electric field strength in a capacitor?
3. How would the charge on the plates change if the diameter of the electrodes was doubled?
4. What is the relationship between capacitance, voltage, and charge in a capacitor?
5. How does introducing a dielectric material affect the charge and electric field in the capacitor?

Tip: Remember to always keep track of units when performing calculations in physics!