Question

A parallel plate capacitor is formed from two circular plates, each of radius 3.10 cm, separated by 3.20 mm. The plates are charged to 11.5 n. A proton is shot from the negative plate to the positive. What launch speed must the proton have to just barely reach the positive plate? O 1.32x10 m/s O 2.64x107 m/s O 3.63x 105 m/s O 5.14x10 m/s

Answer 1

r = 3.1 cm = 3.1 times 10^- 2 m d = 3.2 mm = 3.2 times 10^- 3 m q = 11.5 times 10^- 9 c Electric Field b/w the capacitor E = sigma/alpha epsilon_0 = q/2 pi r^2 epsilon_0 = 11.5 times 10^- 9/2 times 3.14 times (3.1 times 10^- 2)^2 times 8.85 times 10^- 12 E = 11.5 times 10^- 9/534.10 times 10^- 16 = 11.5/5.34 times 10^5 Force on Proton F = qE = ma 1.6 times 10^- 19 times 11.5/5.34 times 10^5 = 1.62 times 10^- 27 times a a = 2.12 times 10^13 v^2 - u^2 = 2ad v = squareroot 2ad = squareroot 2 times 2.12 times 10^13 times 3.2 times 10^- 3 = squareroot 13.56 times 10^12 = 3.68 times 10^5 m/s