I think the problem is broken, I keep getting the same answer, is it wrong? Two
ID: 1653269 • Letter: I
Question
I think the problem is broken, I keep getting the same answer, is it wrong?
Two 2.0-cm-diameter disks face each other, 2.1 mm apart. They are charged to plusminus 11 nC. What is the electric field strength at the midpoint between the centers of the disks? Express your answer to two significant figures and include the appropriate units. A proton is shot from the center of the negative disk toward the center of the positive disk. What launch speed must the proton have to just barely reach the positive disk? Express your answer to two significant figures and include the appropriate units.Explanation / Answer
d = 2.9 cm ; D = 2.9 mm ; q = 17 nC ;
The field between the plates is:
E = sigma/epsilon0
sigma = 11 x 10^-9 / pi x (0.01)^2 = 3.5 x 10^-5 C/m^2
E = 3.5 x 10^-5 C/m^2/8.85 x 10^-12 = 3.955 x 10^6 V/m
Hence, E = 3.96 x 10^6 V/m (upto two decimal places)
From the conservation of energy principle:
Vt - Vb = E D = 3.96 x 10^6 x 2.1 x 10^-3 = 8.32 x 10^3
Kb = q(Vt - Vb)
Kb = 1.6 x 10^-19 x 8.32 x 10^3 = 1.34 x 10^-15
Kinetic energy is:
E = 1/2 m v^2 = Kb
Kb => v = sqrt (2Kb/m)
v = sqrt (2(1.34 x 10^-15)/(1.67x 10^-27) = 1.27 x 10^6 m/s
Hence. v = 1.27 x 10^5 m/s (upto two decimal places)