Question

In the figure 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 +4.15 μC/m2. What is the magnitude of the electron's initial acceleration if it is released at a distance (a) R, (b) R/146, and (c) R/1240 from the center of the disk?

Answer 1

electric field on the axis of a charged disk at a distance x from the center,

E = (sigma/(2*epsilon))*(1 - 1/sqrt(1 + (R^2/x^2)) )

a) at x = R

E = (4.15*10^-6/(2*8.854*10^-12))*(1 - 1/sqrt(2) )

= 68642 N/c

acceleration of the electron, a = q*E/m

= 1.6*10^-19*68641/(9.1*10^-31)

= 1.21*10^16 m/s^2

b) at x = R/146

E = (4.15*10^-6/(2*8.854*10^-12))*(1 - 1/sqrt(1 + 146^2) )

= 232752 N/c

acceleration of the electron, a = q*E/m

= 1.6*10^-19*232752/(9.1*10^-31)

= 4.09*10^16 m/s^2

c) at x = R/1240

E = (4.15*10^-6/(2*8.854*10^-12))*(1 - 1/sqrt(1 + 1240^2) )

= 234168 N/c

acceleration of the electron, a = q*E/m

= 1.6*10^-19*234168/(9.1*10^-31)

= 4.12*10^16 m/s^2