Two parallel plate capacitors have circular plates. The magnitude of the charge on these plates is the same. However, the electric field between the plates of the first capacitor is 2.2e5 N/C, while the field within the second capacitor is 3.8e5 N/C. Determine the ratio r_2/r_1 for the plate radius for the second capacitor to the plate radius for the first capacitor.

6.5e-2 N/C
7.6e-2 N/C
7.6e-1 N/C
0.8e-1 N/C

To find the ratio r_2/r_1 for the plate radius of the second capacitor to the plate radius of the first capacitor, we can use the formula for the electric field between the plates of a parallel plate capacitor:

E = Q / (ε0 * A)

Where:
- E is the electric field
- Q is the charge on the plates
- ε0 is the vacuum permittivity (a constant)
- A is the area of the plates

Since the magnitude of the charge on both capacitors is the same, we can cancel out Q in the equation:

E1 = E2
=> Q / (ε0 * A1) = Q / (ε0 * A2)
=> A2 / A1 = 1

Since the ratio of the areas is 1, that means the ratio of the radii of the plates for the second capacitor to the first capacitor is also 1.

Therefore, the correct answer is r_2/r_1 = 1.