Electrons subjected to a continuous force

In summary, the conversation is about a question regarding electrons and their acceleration under a continuous force. The question asks for the time required to increase the electrons' speed from 0.93c to 99c and the approximate distance traveled in that time. The initial approach using classical mechanics yields different results from using relativistic mechanics. Using relativistic mechanics, the time is calculated to be 2.767E-11 seconds and the distance traveled is 0.016 meters. The difference in results is due to the fact that classical mechanics does not take into account the effects of relativity on high-speed particles.
  • #1
abotiz
72
0
Hi there!

I got some difficulty understanding a question regarding electrons


Electrons which are initially at rest are subjected to a continuous force of 2E-12 N
along a length of 2 miles and reach very near the speed of light.

a) Determine how much time is required to increase the electrons speed from 0.93c to 99c

b) Approximately how far does the electron go in this time? What is approximate about your result?

Because the book don't offer any answers I feel unsure about my answer that follows;

The Impuls = mv1-mv0 Where m is the electrons mass ( 9.109 E-31) and v1=0.99C and v0=0.93C

So I get the Impuls, and then I= F*t I divide the Impuls with the force ( 2E-12) and get the time 8.19E-12 is this right?

And b) I use vt=s where v is 0.99C and get the length 2.43E-3

Have a made a mistake somewhere? Also, I don't understand the second question in b) " What is approximate about your result? "


Thank you
 
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  • #2
You're answer varies from the books because your applying classical mechanics to a relativistic particle.

Try using relativistic mechanics.
 
  • #3
Thanks for your reply!

Okay, so I should be using this instead?
rmom.gif


If I do, I get the time 2.767E-11 s

And the meters it travels would be 0.016 m ( here I used (0.93c+0.99c) multiplied with the time, is this right or should I just have 0.99c)
 

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1. What is the definition of a "continuous force" on an electron?

A continuous force on an electron refers to a force that is constantly applied to an electron over a period of time without any interruptions or breaks.

2. How does a continuous force affect the movement of electrons?

A continuous force can cause electrons to accelerate or decelerate, depending on the direction of the force. It can also change the direction of their movement.

3. What are some examples of continuous forces acting on electrons?

Some examples of continuous forces acting on electrons include electric fields, magnetic fields, and gravitational fields.

4. How are electrons affected by a continuous force in a circuit?

In a circuit, a continuous force, such as an electric field, can cause electrons to flow through the circuit, creating an electric current.

5. Can a continuous force cause electrons to gain or lose energy?

Yes, a continuous force can cause electrons to gain or lose energy. For example, an electric field can give electrons energy as they move through a circuit, while a magnetic field can cause them to lose energy and change direction.

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