Electron accelerated though constant E field

In summary: E field of 1000 V/m can be determined in a) the lab frame and b) the frame of a rocket moving at .99c in the direction of the electric field. This can be achieved by plotting the electron's position as a function of time and applying the Lorentz transformation to the x and t coordinates to get the x' and t' coordinates in the rocket's frame of reference. From there, the velocity and kinetic energy in the rocket's frame can be calculated using the transformed coordinates.
  • #1
deadscientist
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Suppose an electron is initially at rest in a constant E field of 1000 V/m as measured in the lab. Determine the electrons momentum and kinetic energy as a function of time a) in the lab frame b) in the frame of.a rocket moving at .99c in the direction of the electric field. Not quite sure how to approach the problem any suggestions would be greatly appreciated thank you.
 
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  • #2
deadscientist said:
Suppose an electron is initially at rest in a constant E field of 1000 V/m as measured in the lab. Determine the electrons momentum and kinetic energy as a function of time a) in the lab frame b) in the frame of.a rocket moving at .99c in the direction of the electric field.


Not quite sure how to approach the problem any suggestions would be greatly appreciated thank you.
Why not start by plotting position as a function of time? What would that graph look like?

The next step would be to apply the Lorentz transformation to the x and t coordinates to get the x' and t' coordinates in rocket's frame of reference.

Then work out v' in the rocket's frame of reference using those x' and t' coordinates. Then work out v^2 to find kinetic energy.

AM
 

1. What is an electron accelerated through a constant E field?

An electron accelerated through a constant electric field is an electron that is moving due to the influence of a consistent electric force. This can occur when an electric field is created between two charged objects, causing the electron to move towards the positively charged object.

2. How does an electric field accelerate an electron?

An electric field exerts a force on an electron because the electron has a negative charge. This force causes the electron to accelerate in the direction of the electric field.

3. What is the relationship between the strength of the electric field and the acceleration of the electron?

The strength of the electric field is directly proportional to the acceleration of the electron. This means that as the electric field increases, the acceleration of the electron also increases. However, the mass of the electron also plays a role in the acceleration, so a heavier electron will not accelerate as much as a lighter one under the same electric field.

4. Can an electron be accelerated through a constant E field indefinitely?

No, an electron cannot be accelerated through a constant electric field indefinitely. As the electron accelerates, it gains kinetic energy and will eventually reach a velocity where the force of the electric field is balanced by the force of air resistance. At this point, the electron will stop accelerating and will continue to move at a constant speed.

5. What are the practical applications of electron acceleration through a constant E field?

Electron acceleration through a constant electric field has numerous practical applications. It is the basis for many electronic devices, such as cathode ray tubes, electron microscopes, and particle accelerators. It is also used in various industrial processes, such as welding and surface treatment. Additionally, it plays a crucial role in the functioning of solar cells and other renewable energy technologies.

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