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

Answer:

$4.87772175\times 10^{-15}\ C/m^2$

2 mm

Explanation:

$\epsilon_0$ = Permittivity of free space = $8.85\times 10^{-12}\ F/m$

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

v = Velocity of electron = 450 m/s

E = Electric field

$m_e$ = Mass of electron = $9.11\times 10^{-31}\ kg$

$q_e$ = Charge of electron = $1.6\times 10^{-19}\ C$

As the energy of the system is conserved we have

$q_eE\Delta l=\dfrac{1}{2}m_ev^2\\\Rightarrow E=\dfrac{1}{2}\dfrac{m_e}{q_e}\times \dfrac{v^2}{\Delta l}\\\Rightarrow E=\dfrac{1}{2}\dfrac{9.11\times 10^{-31}}{1.6\times 10^{-19}}\times \dfrac{450^2}{2\times 10^{-3}}\\\Rightarrow E=0.00028824609375\ N/C$

For an infinite non conducting sheet electric field is given by

$E=\dfrac{\sigma}{2\epsilon}\\\Rightarrow \sigma=2E\epsilon\\\Rightarrow \sigma=2\times 0.00028824609375\times 8.85\times 10^{-12}\\\Rightarrow \sigma=5.1019558594\times 10^{-18}\ C/m^2$

The surface charge density is $4.87772175\times 10^{-15}\ C/m^2$

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