Let's go through the problem step-by-step to determine the potential difference between the charged plates.
1. Given Values:
- Area of the plates, [tex]\( A = 8.22 \times 10^{-4} \text{ m}^2 \)[/tex]
- Separation between the plates, [tex]\( d = 2.42 \times 10^{-5} \text{ m} \)[/tex]
- Charge on the plates, [tex]\( Q = 5.24 \times 10^{-8} \text{ C} \)[/tex]
2. Constant Value:
- Permittivity of free space, [tex]\( \epsilon_0 = 8.85 \times 10^{-12} \text{ C}^2 / (\text{N} \cdot \text{m}^2) \)[/tex]
3. Formula for Potential Difference:
The potential difference [tex]\( V \)[/tex] between the plates is given by the formula:
[tex]\[
V = \frac{Q \cdot d}{\epsilon_0 \cdot A}
\][/tex]
4. Substitute the given values into the formula:
[tex]\[
V = \frac{(5.24 \times 10^{-8} \text{ C}) \cdot (2.42 \times 10^{-5} \text{ m})}{(8.85 \times 10^{-12} \text{ C}^2 / (\text{N} \cdot \text{m}^2)) \cdot (8.22 \times 10^{-4} \text{ m}^2)}
\][/tex]
5. Simplify the expression:
- Calculate numerator: [tex]\( 5.24 \times 10^{-8} \times 2.42 \times 10^{-5} = 1.26728 \times 10^{-12} \)[/tex]
- Calculate denominator: [tex]\( 8.85 \times 10^{-12} \times 8.22 \times 10^{-4} = 7.2729 \times 10^{-15} \)[/tex]
Therefore,
[tex]\[
V = \frac{1.26728 \times 10^{-12}}{7.2729 \times 10^{-15}}
\][/tex]
6. Division:
[tex]\[
V \approx 174.31 \text{ V}
\][/tex]
So, the potential difference [tex]\( \vee \)[/tex] between the plates is approximately [tex]\( 174.31 \text{ V} \)[/tex].
