Two large and oppositely charged parallel plates are separated by 10mm and orien

Question

Two large and oppositely charged parallel plates are separated by 10mm and oriented parallel to the ground. An electron is projected halfway between the plates and parallel to them with an initial velocity v0= 4.5 X 10^6 m/s. The electron hits the bottom plate 25 mm from where the electron was projected.

A) Which plate is negatively charged? Top or Bottom?

B) What is the surface charge density of the plates if you know that the densities on the top and bottom plate have the same magnitude?

Please give a detailed answer.

Explanation / Answer

length of the plate, l=25mm

separation, d=10mm

initial velocity, vo=4.5*10^6 m/sec

A)

top plate is -Ve ly cherged

B)

here,

time taken, t=l/vo

t=25*10^-3/(4.5*10^6)

t=5.55*10^-9 sec

now,

s=1/2*a*t^2

5*10^-3 =1/2*a*(5.55*10^-9)^2

===> acceleration, a=3.25*10^14 m/sec^2

force on electron,

F=q*E

m*a=q*

and

F=m*a=q*E

m*a=q*(sigma/eo)

9.1*10^-31*3.25*10^14=1.6*10^-19*(sigma)/(8.854*10^-12)

===> sigma=1.64*10^-8 C/m^2

surface charge density, sigma=1.64*10^-8 C/m^2

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