Electrodynamics homework question

In summary, the electron would have an induced charge of -q and the potential zero at slow speeds, but could have an induced charge of -q and the potential greater than zero at fast speeds.
  • #1
yakinc
4
0
Hello
I have a question I got which I've been sitting on for weeks.:grumpy:

I have an electron going through a conducting infinite cylinder of R radius. I need to know what the induced charge is on the cylinder, and the potential, for different speeds of the electron. a) for slow speed v<<c b) for fast speed v=c/constant

thanks :smile:
 
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  • #2
Hi yakinc,

Welcome to the forums! There is lots of great help here, but we make you work for it too. So what are your thoughts so far?
 
  • #3
yakinc said:
Hello
I have a question I got which I've been sitting on for weeks.:grumpy:

I have an electron going through a conducting infinite cylinder of R radius. I need to know what the induced charge is on the cylinder, and the potential, for different speeds of the electron. a) for slow speed v<<c b) for fast speed v=c/constant

thanks :smile:
Unless there is something tricky going on, the induced charge would be -q and the potential zero.
 
  • #4
Meir Achuz said:
Unless there is something tricky going on, the induced charge would be -q and the potential zero.
The tricky thing is with the electron moving at speeds greater than the speed at which electrons can move in the conductor. At such speed, electrons in the conductor may not be not able move quickly enough as the electron moves along the cylinder axis to produce a 0 field everywhere inside the conductor.

AM
 
  • #5
I know that if the electron is not moving we always used green's function.
Let's say I take a certain potential on the cylinder, V (which later can be V(t) ) . Then I can easily get the potential as a function of the coordinates. Then I can derive the fields, and from there maybe use the boundry conditions of the fields to have the field inside and out of the cylinder, then to get to the charge distribution (which is what I really need, not just the total charge). but is it similar in electrodynamics? :shy:
 
  • #6
Calculate the fields in a reference frame where the electron is stationary and then apply lorenz transformation for the fields.
 
  • #7
that's easy.. why didn't i think of that :)

thanks!
 

1. What is Electrodynamics?

Electrodynamics is a branch of physics that studies the interaction between electrically charged particles and their surrounding electric and magnetic fields.

2. What are the main principles of Electrodynamics?

The main principles of Electrodynamics are Coulomb's Law, Gauss's Law, Ampere's Law, and Faraday's Law. These laws describe the behavior of electric and magnetic fields and their effects on charged particles.

3. What are some real-life applications of Electrodynamics?

Electrodynamics has many practical applications in our daily lives, including the functioning of electronic devices such as computers, televisions, and cell phones. It also plays a crucial role in the generation and transmission of electricity.

4. How does Electrodynamics relate to other branches of physics?

Electrodynamics is closely related to other branches of physics, such as classical mechanics, quantum mechanics, and thermodynamics. It provides a framework for understanding the behavior of charged particles and their interaction with electromagnetic fields.

5. What are some common challenges students face when learning about Electrodynamics?

Some common challenges students face when learning about Electrodynamics include understanding the abstract concepts of electric and magnetic fields, solving complex mathematical equations, and visualizing the behavior of charged particles in different scenarios.

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