an electrical deflected CRT has a final anode voltage of 2000V and parallel deflecting plates of 1.5cm long and 5mm apart . IF the screen is 50 cm from the center of the deflecting plates, find beam speed , deflection senstivity pf the tube and deflection factor of the tube

To solve this problem involving a Cathode Ray Tube (CRT), we need to calculate the following:

1. **Beam Speed** (\(v\)) 
2. **Deflection Sensitivity** (\(S\)) 
3. **Deflection Factor** (\(D\)) 

### Given Data:
- **Final anode voltage** (\(V_a\)) = 2000 V
- **Length of deflecting plates** (\(L\)) = 1.5 cm = 0.015 m
- **Distance between deflecting plates** (\(d\)) = 5 mm = 0.005 m
- **Distance from the center of the plates to the screen** (\(D_s\)) = 50 cm = 0.5 m

### 1. **Beam Speed** (\(v\))

The speed of the electron beam is determined by the kinetic energy imparted to it by the accelerating voltage (\(V_a\)). The kinetic energy of the electron is given by:

\[
\frac{1}{2} m_e v^2 = e V_a
\]

Where:
- \(m_e\) is the mass of the electron = \(9.11 \times 10^{-31}\) kg,
- \(e\) is the charge of the electron = \(1.6 \times 10^{-19}\) C,
- \(V_a\) is the final anode voltage.

From the above equation, solving for speed \(v\):

\[
v = \sqrt{\frac{2 e V_a}{m_e}}
\]

Now we can substitute the values and compute the speed.

### 2. **Deflection Sensitivity** (\(S\))

Deflection sensitivity is the deflection per unit deflecting voltage (\(V_d\)). It can be calculated using the formula:

\[
S = \frac{D_s \cdot d}{L \cdot V_a}
\]

Where:
- \(D_s\) is the distance to the screen,
- \(d\) is the separation between the plates,
- \(L\) is the length of the deflecting plates,
- \(V_a\) is the anode voltage.

### 3. **Deflection Factor** (\(D\))

The deflection factor (\(D\)) is the reciprocal of deflection sensitivity:

\[
D = \frac{1}{S}
\]

### Let's calculate these values. I'll begin with the beam speed and proceed to deflection sensitivity and deflection factor.Here are the calculated values:

1. **Beam Speed**: \(v = 2.65 \times 10^7 \, \text{m/s}\) (26.5 million meters per second).
2. **Deflection Sensitivity**: \(S = 8.33 \times 10^{-5} \, \text{m/V}\).
3. **Deflection Factor**: \(D = 12000 \, \text{V/m}\).

Would you like more details or have any further questions?

Here are 5 related questions that expand on this topic:
1. How would increasing the final anode voltage affect the beam speed?
2. How does the distance between the deflecting plates influence deflection sensitivity?
3. What role do the deflecting plates play in a CRT system?
4. Can we compute the angle of deflection based on these values?
5. How would changing the screen distance affect the deflection factor?

**Tip:** Higher deflection sensitivity means the CRT is more responsive to changes in deflection voltage, making it easier to control the electron beam's movement.

An electrical deflected CRT has a final anode voltage of 2000V and parallel deflecting plates of 1.5cm long and 5mm apart. If the screen is 50cm from the center of the deflecting plates, find beam speed, deflection sensitivity of the tube, and deflection factor of the tube.

This solution explains how to calculate the beam speed, deflection sensitivity, and deflection factor for a Cathode Ray Tube (CRT) with a final anode voltage of 2000V, deflecting plates 1.5cm long and 5mm apart, and a screen distance of 50cm. Learn about key physics concepts like kinematics and electromagnetism.

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