In the figure below, an electron (e) is to be released from rest on the central
ID: 1524634 • Letter: I
Question
In the figure below, an electron (e) is to be released from rest on the central axis of a uniformly charged disk of radius R. The surface charge density on the disk is +4.21 C/m2.
(a) What is the magnitude of the electron's initial acceleration if it is released at a distance R from the center of the disk?
m/s2
(b) What is the magnitude if it is released at a distance R/100 from the center?
m/s2
(c) What is the magnitude if it is released at a distance R/1000 from the center?
m/s2
(d) Why does the acceleration magnitude increase only slightly as the release point is moved closer to the disk?
Explanation / Answer
a) Here, electric field = [sigma /(2 eps0)] [ 1- D / sqrt(R^2+D^2)]
Thus, electric field = [4.21 * 10-6 /(2 * 8.85 * 10-12)] [ 1- R / sqrt(R^2+R^2)]
= 69640.16 N/C
the magnitude of the electron's initial acceleration = (1.6 * 10-19 * 69640.16)/(9.11 * 10-31)
= 1.223 * 1016 m/s2
b) Thus, electric field = [4.21 * 10-6 /(2 * 8.85 * 10-12)] [ 1- R/100 / sqrt(R^2+(R/100)^2)]
= 235474.69 N/C
the magnitude of the electron's initial acceleration = (1.6 * 10-19 * 235474.69)/(9.11 * 10-31)
= 4.13 * 1016 m/s2
c) Thus, electric field = [4.21 * 10-6 /(2 * 8.85 * 10-12)] [ 1- R/1000 / sqrt(R^2+(R/1000)^2)]
= 237615.25 N/C
the magnitude of the electron's initial acceleration = (1.6 * 10-19 * 237615.25 )/(9.11 * 10-31)
= 4.173 * 1016 m/s2
d) the acceleration magnitude increase only slightly as the release point is moved closer to the disk due to larger radius as compared to the distance .