# Magnetic field caused by an accelerating electron?

## Homework Statement

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. "

F=q(v x B)

## 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?

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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.

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.
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...

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

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

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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 !

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 !
!!! 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 :)

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.

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

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

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

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?

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

Or in other words electrons traveling in a straight line

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

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?

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?
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?

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

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. :)

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

this could be done with concentric circles or a corkscrew shape. depending on how you want to show it.

just make sure and draw the direction of the field.

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. :)
But would this not be the case for an electron moving at a constant speed rather than an accelerating one?

yes. to show this you just increase the space between each snapshot the B field still is a counter-clockwise wheel around the electron. it travels with the electron in space because its part of it. It doesn't stretch or anything so the b-field is the same. but as I increases (the speed of the electron) the B field increases in magnitude. Faster electrons = stronger field.

same shape and direction just stronger. You could show this by having more concentric arrows as time goes on. oh and by "I" I mean current or speed of electrons.