An electron traveling in the -x direction approaches a capacitor consisting of t

Question

An electron traveling in the -x direction approaches a capacitor consisting of two large, oppositely charged metal plates. The circular plates are 3 cm apart and each has a radius of 4.2 m. (Only a small portion near the center is shown.) The electron enters the capacitor through a small hole in one of the plates at location A with a kinetic energy of 6.2 Times 10^-17 J. It exits through a small hole at location B with a kinetic energy of 1.4 Times 10^-17 J. On the diagram, draw an arrow indicating the direction of the electric field within the gap between the capacitor plates, and indicate which plate is positively charged and which is negatively charged. What is the potential difference Vb - Vk? Clearly show all steps in your work. What is the magnitude of the charge on one of the plates? Clearly show all steps in your work.

Explanation / Answer

a) if electron goes in the direction of electric field its kinetic decreases.

so electric field direction is from A to B.

A is positive charged plate and B is negative charged plate.

b) Work done by electric field = change in KE

-1.6 x 10^-19 x V = (1.4 x 10^-17) - (6.2 x 10^-17)

V = 300 V

and vb - va = - 300 V

C) Capacitance of this plate system = C

C = e0 A / d

A = pi x 4.2^2 = 55.42 m^2

C = 8.854 x 10^-12 x 55.42 / (0.03)

C = 1.64 x 10^-8 F

Q = CV = 4.91 x 10^-6 C

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