Final answer:
To find the capacitor plate area, convert the electric field to V/m, calculate the plate separation using E = V/d, and then use C = ε0A/d to solve for the area.
Step-by-step explanation:
The student is asking how to determine the area of the plates of a capacitor, given that the capacitor with no dielectric has an electric field of 53 kV/mm between the plates and the voltage across the capacitor is 1.4 V. To find the plate area, we can use the capacitance formula C = ε0A/d, where C is the capacitance, ε0 is the permittivity of free space, A is the area, and d is the separation between the plates. The electric field E is related to the voltage V and separation d by E = V/d. First, we need to convert the electric field to V/m from kV/mm by multiplying by 106, which gives us E = 53 x 106 V/m.
The separation between the plates d can be found using the electric field formula, d = V/E. Once we have d, we can solve for A using the capacitance formula with the given capacitance of 28 F. We know that ε0 = 8.85 x 10-12 F/m for free space. After substitution and rearrangement, the area A can be found by multiplying capacitance C by plate separation d and dividing by the permittivity ε0. This will give us the required plate area