Question

Two identical closely spaced circular disks form a parallel-plate capacitor. Transferring 2.0×10⁹ electrons from one disk to the other causes the electric field strength between them to be 1.3×10⁵ N/C .

What are the diameters of the disks?

Answer 1

Given,

N = 2 x 10^9 ; E = 1.3 x 10^5 N/C

We know that

C = e0 A/d

E = V/d => V = E d

Q = CV

Q = e0 A/d x Ed

Q = e0 A E = e0 pi d^2/4

solving for D

D^2 = 4 Q/(pi e0 E)

D = sqrt (4 Q/(pi e0 E))

D = sqrt [4 x 2 x 10^9 x 1.6 x 10^-19/(3.14 x 8.85 x 10^-12 x 1.3 x 10^5)] = 0.0188 m

Hence, D = 0.0188 m = 1.88 cm