2. Using conservation of energy, show that the speed v of an electron leaving your "electron gun" can be written in terms of the electron accelerating potential V, electron charge e and electron mass me as: v= 2eV me (5)
2. Using conservation of energy, show that the speed v of an electron leaving your "electron gun" can be written in terms of the electron accelerating potential V, electron charge e and electron mass me as: v= 2eV me (5)
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![**Problem 2:**
Using conservation of energy, **show** that the speed \( v \) of an electron leaving your "electron gun" can be written in terms of the electron accelerating potential \( V \), electron charge \( e \), and electron mass \( m_e \) as:
\[
v = \sqrt{\frac{2eV}{m_e}}
\]
*(Equation 5)*](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Facfb296d-c42b-4e28-876a-1baf5375f9c9%2F4ae8cb22-d794-4a30-ba44-1aa3beff6010%2Fhtbyhof_processed.png&w=3840&q=75)
Transcribed Image Text:**Problem 2:**
Using conservation of energy, **show** that the speed \( v \) of an electron leaving your "electron gun" can be written in terms of the electron accelerating potential \( V \), electron charge \( e \), and electron mass \( m_e \) as:
\[
v = \sqrt{\frac{2eV}{m_e}}
\]
*(Equation 5)*
![**Text Transcription:**
be perpendicular to the electron velocity, causing the electrons to move in a circular path. By varying the current going through the Helmholtz coils you will be able to vary the applied magnetic field and thus change the radius of the electron paths. The magnetic field will be produced using "Helmholtz coils" that produce a magnetic field strength (at the center of the coil configuration) given by:
\[
B = \frac{8}{5\sqrt{5}} \frac{\mu_0 IN}{R},
\]
where \( R \) is the radius of the coils, \( N \) is the number of turns per coil (\( N = 124 \) in your set-up), \(\mu_0 = 4\pi \times 10^{-7} \, \text{T} \cdot \text{A/m}\), and \( I \) is the current flowing through the coils.
---
**Graph/Diagram Explanation:**
*Figure 2:*
(a) *Schematic Diagram of the Vacuum Tube:*
- This diagram illustrates the setup used to determine the value of \( e/m_e \), which is the charge-to-mass ratio of the electron.
- The setup includes a helium-filled vacuum tube.
- The electron gun emits electrons that follow a circular path, depicted in blue, due to the influence of magnetic fields produced by Helmholtz coils.
- Key components highlighted include the helium-filled vacuum tube, electron gun, electron's path, and deflection plates.
(b) *Cathode and Anode Arrangement of the Electron Gun:*
- This schematic details the arrangement of the electron gun components.
- It consists of a cathode (marked with a negative sign), an anode (marked with a positive sign), a grid, and a heater.
- The electron movement direction within this setup is indicated by a blue arrow moving towards the anode.
- The diagram also highlights the location of deflection plates used to influence electron direction.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Facfb296d-c42b-4e28-876a-1baf5375f9c9%2F4ae8cb22-d794-4a30-ba44-1aa3beff6010%2Fixseoh_processed.png&w=3840&q=75)
Transcribed Image Text:**Text Transcription:**
be perpendicular to the electron velocity, causing the electrons to move in a circular path. By varying the current going through the Helmholtz coils you will be able to vary the applied magnetic field and thus change the radius of the electron paths. The magnetic field will be produced using "Helmholtz coils" that produce a magnetic field strength (at the center of the coil configuration) given by:
\[
B = \frac{8}{5\sqrt{5}} \frac{\mu_0 IN}{R},
\]
where \( R \) is the radius of the coils, \( N \) is the number of turns per coil (\( N = 124 \) in your set-up), \(\mu_0 = 4\pi \times 10^{-7} \, \text{T} \cdot \text{A/m}\), and \( I \) is the current flowing through the coils.
---
**Graph/Diagram Explanation:**
*Figure 2:*
(a) *Schematic Diagram of the Vacuum Tube:*
- This diagram illustrates the setup used to determine the value of \( e/m_e \), which is the charge-to-mass ratio of the electron.
- The setup includes a helium-filled vacuum tube.
- The electron gun emits electrons that follow a circular path, depicted in blue, due to the influence of magnetic fields produced by Helmholtz coils.
- Key components highlighted include the helium-filled vacuum tube, electron gun, electron's path, and deflection plates.
(b) *Cathode and Anode Arrangement of the Electron Gun:*
- This schematic details the arrangement of the electron gun components.
- It consists of a cathode (marked with a negative sign), an anode (marked with a positive sign), a grid, and a heater.
- The electron movement direction within this setup is indicated by a blue arrow moving towards the anode.
- The diagram also highlights the location of deflection plates used to influence electron direction.
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