A capacitor consists of plates 3 m in radius, separated by a distance of 6 mm. T

Question

A capacitor consists of plates 3 m in radius, separated by a distance of 6 mm. The left plate of the capacitor has a charge of-7x10-7 C. (a) what is the potential difference le-Vo? Show all steps in your work. (b) What is the potential difference Va-Va? Show all steps in your work. (e) What is the potential difference Vc-Va? Show all steps in your work (d) A moving electron enters the capacitor through a tiny hole in the right plate. Its initial velocity is such that it passes through location A, and a short time later it reaches location C. What is the change in kinetic energy of the electron between location A and location C? (Remember that the gravitational force on the electron is negligible compared to electric forces.) Show all steps in your work. (e) What is the magnitude and direction of the electric feld in the region between the plates? 15

Explanation / Answer

Given,

r = 3 m ; Q = 7 x 10^-7 C

a)We know that

Q = CV => V = Q/C

C = e0 A/d

C = 8.85 x 10^-12 x 3.14 x 3^2/6 x 10^-3 = 4.17 x 10^-8 F

V = 7 x 10^-7/4.17 x 10^-8 = 16.8 V

Hence, Vc - Vb = 16.8 V

b)The points B and A are at the same potential.

Hence, Vb - Va = 0 V

c)Vc - Vb = Vc - Va = 16.8 V

d)the change in kinetic energy will be:

delta-KE = q V

delta-KE = 1.6 x 10^-19 x 16.8 = 2.69 x 10^-18 J

Hence, delta-KE = 2.69 x 10^-18 J

e)E = V/d

E = 16.8/6 x 10^-3 = 2.8 x 10^3 V/m

Hence, E = 2.8 x 10^3 V/m

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