Question

I have no clue: Two parallel plate capacitors have circular plates. The magnitude of the charge on these plates are the same. However, the electric field between the plates of the first capacitor is 2.2 x 10^5 N/C, while the field within the second capacitor is 3.8x 10^5 N/C. Determine the ratio r2/r1 of the plate radius for the second capacitor to the plate radius for the first capacitor.

Answer 1

Assume both are air-gap capacitors; otherwise the unknown dielectric constant of the material between the plates complicates the problem.

You also need to assume that the width of the air gap is the same for each; otherwise another variable is introduced.

The electric field between the plates is proportional to the charge density per area.

The first capacitor has 2.2/3.8 = 57.9% of the E-field of second capacitor

Q1/(pi*R1^2) = Q2/(pi*R2^2)
= 0.579 Q1/(pi*R2^2)

R2^2/R1^2 = 0.579
R2/R1 = 0.761

The second capacitor has a smaller area so that it can have a higher charge density and higher E-field