Question

An electron initially 3.00 mm from a nonconducting infinite sheet of uniformly distributed charge is fired toward the sheet. The electron has an initial speed of 450 m/sm/s and travels along a line perpendicular to the sheet. When the electron has traveled 2.00 mm , its velocity is instantaneously zero, and it then reverses its direction.

A- What is the surface charge density on the sheet?B- Given the same initial velocity, from what distance should the electron be fired if it is to just reach the sheet?

Answer 1

`4.87772175* 10^(-15)\ C/m^2`

2 mm

Step-by-step explanation:

`\epsilon_0` = Permittivity of free space =
`8.85* 10^(-12)\ F/m`

`\Delta l` = Distance charge traveled = 2 mm

v = Velocity of electron = 450 m/s

E = Electric field

`m_e` = Mass of electron =
`9.11* 10^(-31)\ kg`

`q_e` = Charge of electron =
`1.6* 10^(-19)\ C`

As the energy of the system is conserved we have

`q_eE\Delta l=(1)/(2)m_ev^2\\\Rightarrow E=(1)/(2)(m_e)/(q_e)* (v^2)/(\Delta l)\\\Rightarrow E=(1)/(2)(9.11* 10^(-31))/(1.6* 10^(-19))* (450^2)/(2* 10^(-3))\\\Rightarrow E=0.00028824609375\ N/C`

For an infinite non conducting sheet electric field is given by

`E=(\sigma)/(2\epsilon)\\\Rightarrow \sigma=2E\epsilon\\\Rightarrow \sigma=2* 0.00028824609375* 8.85* 10^(-12)\\\Rightarrow \sigma=5.1019558594* 10^(-18)\ C/m^2`

The surface charge density is
`4.87772175* 10^(-15)\ C/m^2`

The surface charge density is constant throughout so the electron should be fired from the distance of 2 mm