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Electric field between two plates..?
In a cathode-ray tube (CRT), an electron travels in a vacuum and enters a region between two "deflection" plates which have equal and opposite charges. The dimensions of each plate are 12 cm by 3 cm, and the gap between them is 2.5 mm (not to scale in the diagram, note periods are just place holders to line up drawing).
....y
.....I
.....I
.....I_ _ _ _ _ _ _x
..../....plate........./.3cm.....the other plate is located above the
.../___________/.............one pictured and is parallel
../....12 m.........................with gap 2.5mm between
z
During a 0.001 s interval while it is between the plates, the change of the momentum of the electron DeltaP is < 0,-7.20e-17,0 > kg m/s.
What is the electric field between the plates?
Hint: remember the Momentum Principle (the relationship between Impulse and change in momentum.)
E = < 0,...., 0 > N/C
What is the charge (both magnitude and sign) of the upper plate?
q = ........C
Momentum change ΔP = Ft; solve for F
F = EQ; look up Q for 1 electron, solve for E
Now solving for plate charge:
Capacitance C = k*e0*area/separation, dielectric constant k = 1, permittivity e0 = 8.8542E-12 F/m
V = E*separation
Q = VC
Thus (dropping k) we can say Q = E*e0*area (see ref.)
ΔP and F are neg. thus upper plate is charged neg. wrt lower plate.
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