Question

An electron is fired directly toward the center of a large metal plate that has excess negative charge with surface charge density 6.00×10^-6 C/ m². If the initial kinetic energy of the electron is 130 eV and if the electron is to stop (owing to electronstatic repulsion from the plate) just as it reaches the plate, how far from the plate must it be fired?

What is the magnitude of the acceleration?

Answer 1

step;1

Given that

Charge density =6*10^-6 C/m^2

K.Ei=130eV=130*1.6*10^-19=208*10^-19 J

step;2

now we find the electric field

electric field E=6*10^-6/2*8.85*10^-12

                   =3.4*10^5 N/c

step;3

now we find the acceleration

acceleration a=1.6*10^-19*3.4*10^5/9.1*10^-31

                    =0.6*10^17 m/s^2

step;4

now we find the time

208*10^-19=(3.4*10^5)^2*(1.6*10^-19)^2*t/2*9.1*10^-31

3785.6*10^-31=29.6*10^-9*t

time t=127.9*10^-22 sec

distance s=1/2*0.6*10^17*(127.9*10^-22)^2

              =4907.5*10^-27 m