# Calculating Electron Deflection in CRT

• c0der
In summary: Therefore, they are only considering the deflection after the electrons pass clear of the plates. In summary, using Newton's 2nd Law and kinematics, the deflection of electrons in a cathode-ray tube can be determined in terms of the dimensions of the voltage plate and tube. However, the solution does not take into account the slight deflection between the plates, as it is negligible compared to the overall deflection.
c0der

## Homework Statement

In the cathode-ray tube, electrons having a mass m
are emitted from a source point S and begin to travel
horizontally with an initial velocity v0. While passing
between the grid plates a distance l, they are subjected to a
vertical force having a magnitude eV/w, where e is the
charge of an electron, V the applied voltage acting across
the plates, and w the distance between the plates. After
passing clear of the plates, the electrons then travel in
straight lines and strike the screen at A. Determine the
deflection d of the electrons in terms of the dimensions of
the voltage plate and tube. Neglect gravity which causes a
slight vertical deflection when the electron travels from S to
the screen, and the slight deflection between the plates.

See attachment for picture

∑Fy = may

vy = ayt

## The Attempt at a Solution

By Newton's 2nd Law,

ay = eV/mw from 0 to l

By kinematics t1 = l/v0
t2 = t1 + L/v0 = l/v0 + L/v0

From 0 to l, by kinematics:

y1 = 1/2*eV/mw*(l/v0^2)
(v1)y = eV/mw*l/v0

Hence, from l to L where ay is zero

y2 = d = 1/2*eV/mw*l^2/v0^2 + eV/mw*L/v0

It appears the solution is missing the left term I keep getting, any idea why?

#### Attachments

• Hibbeler 13-34.png
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The solution is missing that term because they are neglecting the slight deflection between the plates, as mentioned at the end of the problem statement.

## 1. How is electron deflection calculated in a CRT?

Electron deflection in a CRT is calculated using the formula F = qE, where F is the force of deflection, q is the charge of the electron, and E is the strength of the electric field. This formula takes into account the voltage applied to the deflection plates and the distance between them.

## 2. What factors affect electron deflection in a CRT?

The main factors that affect electron deflection in a CRT are the voltage applied to the deflection plates and the distance between them. The strength of the electric field created by the voltage determines the amount of deflection, and the distance between the plates determines the angle of deflection.

## 3. How does the angle of deflection in a CRT affect the display?

The angle of deflection in a CRT affects the display by determining the position of the electron beam on the screen. The electron beam scans across the screen in a series of horizontal lines, and the angle of deflection determines the starting position of each line. This ultimately affects the overall picture quality and clarity.

## 4. Can electron deflection be adjusted in a CRT?

Yes, electron deflection can be adjusted in a CRT by changing the voltage applied to the deflection plates. This can be done manually or automatically by the circuitry within the CRT. Adjusting the deflection allows for precise control over the electron beam and can improve the quality of the displayed image.

## 5. Why is electron deflection important in CRT technology?

Electron deflection is crucial in CRT technology because it allows for the creation of images on the screen. By manipulating the electron beam, the CRT can produce a wide range of shapes and colors, making it a versatile display technology. Without electron deflection, CRTs would not be able to function as a display device.

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