As mentioned in the previous problem, capacitor is a device with two parallel pl
ID: 1778186 • Letter: A
Question
As mentioned in the previous problem, capacitor is a device with two parallel plates with opposite charges (one charged to +Q, the other to –Q), which produces a uniform electric field between the plates. While capacitors are often used in electric circuits, they also have other applications as well, due to the nice uniform electric field. For example, that uniform electric field is useful for steering the path of charged particles. Cathode Ray Tube televisions use capacitors to steer electrons to different parts of the screen, as part of the process of making the picture on the screen. The picture below shows this process, with an electron traveling to the right between capacitor plates (the plates are not drawn to scale – the distance between the plates is much smaller than the size of the plates themselves. You’re going to try to analyze the deflection due to the electric field. Let’s say the capacitor is 10 cm long (D0 in the left picture), and an electron enters the region between the plates with a speed of 106 m/s. In order to get a deflection of 1 mm (d in the picture) by the time the electron leaves the plates, what must the electric field between the plates be?Explanation / Answer
Given
capacitor of length l = 10 cm =0.1 m
electron moving with velocity v = 106 m/s
deflection is 1 mm ,
here the electron moving in the electric field so that the force acting on it is
m*a = E*q
a = E*q/m along y direction
and the time taken by the electron when it leave the capacitor is t = d/v = 0.1/106 s = 0.000943396 s = 0.943396 ms
by using equations of motions
along vertical direction
y = 0.5*at^2
y = 0.5*E*q/m *t^2
E = y*t^2*m*2/q
E = (0.001*0.000943396^2*9.11*10^-31*2)/(1.6*10^-19) N/C
E = 1.013483*10^-20 N/C
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