How Does an Electron's Path Deflect Over a Charged Plate?

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SUMMARY

The discussion focuses on calculating the vertical deflection of an electron with a kinetic energy of 5000.0 eV as it travels over a charged plate with a surface charge density of +2.0 μC m-2. The calculations involve determining the electron's velocity, time of flight, electric field strength, force, acceleration, and ultimately the vertical deflection. The final computed deflection is 0.00226 meters, but the contributor expresses uncertainty about the accuracy of this result, indicating a potential error in the setup or calculations.

PREREQUISITES
  • Understanding of kinetic energy and its conversion to velocity
  • Familiarity with electric fields and surface charge density
  • Knowledge of force and acceleration calculations in physics
  • Basic principles of motion and deflection in electric fields
NEXT STEPS
  • Review the calculation of electric field strength using the formula E = σ/(2ε0)
  • Examine the relationship between force, charge, and electric field in F = qE
  • Study the equations of motion, particularly d = 0.5at2 for vertical deflection
  • Investigate the impact of relativistic effects on electron motion at high velocities
USEFUL FOR

Physics students, educators, and professionals in fields related to electromagnetism and particle physics will benefit from this discussion, particularly those interested in the behavior of charged particles in electric fields.

eltel2910
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An electron with a kinetic energy 5000.0 eV (1 eV = 1.602×10-19 J) is fired horizontally over a charged plate with surface charge density +2.0 μC m-2. Taking the positive direction to be upwards (away from plate), what is the vertical deflection of the electron after it has traveled a horizontal distance 2.0 cm?

Here is my work:

Find V of electron - KE = .5mV ---> 41934557 = Velocity

time = s/V ----> .02m/41934557 --------> 4.769e^-10 = time

electric field E = sigma/2*Eo -----> 2.0e^-6/(2*(8.85*10^-12) ---->112994 = E

Force = q*E ------>(1.602*10^-19)(112994) ------->1.810e^-14 = F

acceleration = F/m -------> 1.810e^-14/(9.11*10^-31) = 1.98e^16. 9.11*10^-31=mass of one proton.

vertical deflection = d=.5at^2 --------> .00226=.5(1.98e^16)(4.769e^-10)^2

I come up with .00226 meters, but "the man" still says I'm wrong

Can you see anything wrong with my set up??
 
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eltel2910 said:
Find V of electron - KE = .5mV ---> 41934557 = Velocity

time = s/V ----> .02m/41934557 --------> 4.769e^-10 = time

electric field E = sigma/2*Eo -----> 2.0e^-6/(2*(8.85*10^-12) ---->112994 = E

Force = q*E ------>(1.602*10^-19)(112994) ------->1.810e^-14 = F

acceleration = F/m -------> 1.810e^-14/(9.11*10^-31) = 1.98e^16. 9.11*10^-31=mass of one proton.

vertical deflection = d=.5at^2 --------> .00226=.5(1.98e^16)(4.769e^-10)^2

Can't see anything wrong except the one that has been highlighted.
 

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