# Magnetic field caused by an accelerating electron?

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1. Jan 12, 2015

### 21joanna12

1. The problem statement, all variables and given/known data
I am trying to answer the question:
"An electron is accelerated in an evacuated chamber. Sketch lines that illustrate how the magnetic field produced by the electron will vary with time. "

2. Relevant equations
F=q(v x B)

3. The attempt at a solution
I cannot find a sketch of this anywhere. I would think that you would just sketch it as a greater number of concentric circles being produced as the electron accelerates? Any ideas?

2. Jan 12, 2015

### scott mcleod jr

Im sure seeing the level of problem this is that you are familiar with the Right Hand Rule? If not this describes how a moving particles velocity, B field and the Force vectors relate.

3. Jan 12, 2015

### 21joanna12

I am familiar with the right hand rule. I am doing A Level Physics (equivalent of final year of high school), although this is from a physics olympiad paper so I am not sure exactly what level of difficulty this would be. It is one of the ''warm up questions' to a much longer question which I had no trouble with, but this part does not have an answer...

4. Jan 12, 2015

### scott mcleod jr

Good. If the particle is traveling in a straight line and it is accelerating then your velocity vector is changing. Now if you space out each of your drawings as being in equal times, the particle should be traveling in greater and greater distances in equal time. Sooo... your magnetic field should also be changing in spacing. The real kicker is does the bfield change in magnitude with respect to the increase in velocity

5. Jan 12, 2015

### scott mcleod jr

Think about what values are constant in your main equation and what the relationship is between perpendicular vectors.

6. Jan 12, 2015

### BvU

I'm puzzled. The relevant equation is about the force felt by a moving charge, not about a B field generated by a moving charge !

7. Jan 12, 2015

### 21joanna12

!!! You're right! I apologise! I realise now that I have never actually learned about the B field produced by a moving charge, only the force felt by a moving charge in a B field!
Thank you for pointing this out :)

8. Jan 12, 2015

### scott mcleod jr

No. He is asking what happens to the magnetic field (B field) over time as the particle increases in speed (accelerates). He is supposed to draw the B Field (magnetic field). But V is crossed with B so they are perpendicular so over time increasing the V (accelerating) has no effect on the magnitude of the B field just the spacing between lines.

9. Jan 12, 2015

### scott mcleod jr

Ah I see what you are saying, yeah the equation doesn't match. :) lol

10. Jan 12, 2015

### scott mcleod jr

I was trying to visualize it and it didn't make sense

11. Jan 12, 2015

### 21joanna12

So I suppose I should be using $B=\frac{\mu_0}{4\pi}\frac{qvsin(\theta)}{r^2}$....

12. Jan 12, 2015

### 21joanna12

I just realised that I don't actually know HOW the moving particle produces a magnetic field in the sense that I am not sure whether the magnetic field emanates from the particle like ripples when you drop a pebble into water (but in this case the waves would spread ot at the speed of light) or whether the field is just there? My guess is that it is the former, in which case the diagram of the electron accelerating would look like a series of circle that are doppler shifted- so the magnetic field is stronger in front of the electron than behind because you have a greater magnetic field line density there?

Am I along the right lines?

13. Jan 12, 2015

### scott mcleod jr

Lets reset. Do you know the other right hand rule for the b field of a particle traveling through a wire?

14. Jan 12, 2015

### scott mcleod jr

Or in other words electrons traveling in a straight line

15. Jan 12, 2015

### 21joanna12

Yes

16. Jan 12, 2015

### scott mcleod jr

so if your thumb is in the direction of the direction of travel. The b field curls counter-clockwise as you are looking head on at it. so if its accelerating what do you think the shape of the path of the b field is?

17. Jan 12, 2015

### 21joanna12

If the electron was moving at a constant speed, then I think the B field would look like a cone with the field going out at the speed of light from where the electron is at any moment in time. But since the electron is accelerating, I am not sure. I think the B field would still look like a cone because the field would not move out any faster, however it would be getting progressively 'denser' with field lines- i.e. the field represented by the cone would be getting stronger?

18. Jan 12, 2015

### 21joanna12

I think I may be over-complicating this...

19. Jan 12, 2015

### scott mcleod jr

yeah lol. I realized that a little late too :).
It should be a corkscrew shape as it travels, just like if you followed an individual electron through a wire. :)

20. Jan 12, 2015

### scott mcleod jr

draw the path of the electron and then the path of the field around it over time