An electron in a computer monitor enters midway between two parallel oppositely

Question

An electron in a computer monitor enters midway between two parallel oppositely charged plates, as shown in the figure . The initial speed of the electron is 6.95×107 m/s and its vertical deflection (d) is 4.70 mm.

A) What is the magnitude of the electric field between the plates?
B) Determine the magnitude of the surface charge density on the plates in C/m^2.

An electron in a computer monitor enters midway between two parallel oppositely charged plates, as shown in the figure . The initial speed of the electron is 6.95107 m/s and its vertical deflection (d) is 4.70 mm. A) What is the magnitude of the electric field between the plates? B) Determine the magnitude of the surface charge density on the plates in C/m^2.

Explanation / Answer

Time between plates = 0.10m / 6.60^7m/s .. .. t = 1.515^-9s

Vertical acceleration from d = ut + ½.at² .. (u=0 vertically)
a = 2d/t² .. a = (2 x .0047m)/(1.515^-9s)² .. a = 4.10^15 m/s

Force on electron = (Me x a) = (9.10*-31kg)(4.10^15m/s²) .. .. Fe = 3.73^-15 N

Field, E = Fe(N)/1.60^-19C = 3.73^-15N / 1.60^-19C .. .. E = 2.33^4 N/C

(B) Using, E = / .. (a very useful relationship to remember !)
.. [ = charge density, = permittivity]
.. = E.
.. = (2.33^4 N/C)(8.85^-12F/m) .. .. = 2.06^-7 C/m²

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