Expression of acceleration with electric field increase

[DandelionTheory]

I'm bad at math. I would like to ask how to express the change in velocity of an electron in an increasing electric field with constant magnetic field (separate magnet, I need electron path not force on the system)

I learned from reading about magnetrons that the radius of the curved path of an electron in an electric field with perpendicular magnetic field is expressed R=(mv/qB)

Is the change in radius due to the change in velocity expressed dR=(mdv/qB)?

How do I express a change in velocity of an electron in an increasing electric field? 

-DT

Edited September 8, 2020 by DandelionTheory

[joigus]

12 minutes ago, DandelionTheory said:

I would like to ask how to express the change in velocity of an electron in an increasing electric field with constant magnetic field (separate magnet,

A varying electric field will induce a varying magnetic field, so no, you can't have an increasing electric field with constant magnetic field.

[DandelionTheory]

31 minutes ago, joigus said:

A varying electric field will induce a varying magnetic field, so no, you can't have an increasing electric field with constant magnetic field.

I get the magnetic field of the electron will increase with velocity, it however shouldn't increase the magnetic field of an external magnet, right?

[joigus]

You can keep sustain a constant magnetic field from an external magnet, but if you set up an increasing electric field, it will generate an additional increasing magnetic field of its own.

The rate of change of the electric field's flux through a surface giving you the circulation of the magnetic field around the surface's contour.

If you set up the electric field's flux to increase linearly with time, you can arrange for the additional magnetic circulation to be constant.

Edited September 8, 2020 by joigus
Addition+eliminated ambiguity in phrase

[DandelionTheory]

13 minutes ago, joigus said:

You can keep sustain a constant magnetic field from an external magnet, but if you set up an increasing electric field, it will generate an additional increasing magnetic field of its own

Understood. I expected that.

16 minutes ago, joigus said:

you set up the electric field's flux to increase linearly with time, you can arrange for the additional magnetic circulation to be constant

What?

I was looking for the method to express the increase in velocity of an electron in an increasing parallel electric field with a perpendicular magnetic field.i didn't ask about the electrons magnetic field change. 

[joigus]

3 minutes ago, DandelionTheory said:

Understood. I expected that.

What?

I was looking for the method to express the increase in velocity of an electron in an increasing parallel electric field with a perpendicular magnetic field.i didn't ask about the electrons magnetic field change. 

I'm not talking about the electron's magnetic field. I'm talking about your increasing electric field. You cannot have ANY increasing electric field without it generating a magnetic field wrapped around its field lines. Do you understand? If you don't, this conversation will become pointless very quickly.

Of course an electron acts on itself when it radiates; that's called radiation reaction. But that's not what I'm talking about here. Even in the absence of a magnet, and in the absence of self-interactions, your increasing electric field will generate other magnetic field lines around the electron's velocity, and the electron will spiral out of its initial direction. When I have more time, maybe I can draw a picture for you. You must identify all the field sources to account for all the E and B fields.

Then there is your external magnet. That will further complicate the motion. It's got nothing to do with electron's self-interaction. You would have to accelerate the electron considerably before you had any radiation reaction (self-interaction) on the electron.

[DandelionTheory]

6 minutes ago, joigus said:

I'm not talking about the electron's magnetic field. I'm talking about your increasing electric field. You cannot have ANY increasing electric field without it generating a magnetic field wrapped around its field lines. Do you understand? If you don't, this conversation will become pointless very quickly.

Yes, it's expected. Any charged particles motion has a magnetic field, an increasing velocity of that particle would increase it's magnetic field; also true for all charges in the circuit. 

I don't understand why we are not on the same page. I read the force on a charge is due to an applied external electric field and curved by an applied external magnetic field. No where does it say anything about lorentz forces due to the electrons own magnetic field.

[joigus]

5 minutes ago, DandelionTheory said:

No where does it say anything about lorentz forces due to the electrons own magnetic field.

Will you just read what I wrote? What's this, an internet forum version of candid camera?

[DandelionTheory]

1 minute ago, joigus said:

Will you just read what I wrote? What's this, an internet forum version of candid camera?

I guess I need to wait for the edit window to expire. My apologies.

[joigus]

9 minutes ago, DandelionTheory said:

Yes, it's expected.

Well, maybe it's expected, but you don't seem to expect it:

1 hour ago, DandelionTheory said:

change in velocity of an electron in an increasing electric field with constant magnetic field (separate magnet,

Don't you see the inconsistency? You've got two independent sources of magnetic field here, and nobody's talking about "own magnetic field." Well, only you are.

[DandelionTheory]

5 minutes ago, joigus said:

Well, maybe it's expected, but you don't seem to expect it:

Okay.

9 minutes ago, joigus said:

You've got two independent sources of magnetic field here,

Right. You read the word problem correctly. I'm asking how to express the change in velocity when the applied magnetic field is constant and the electric field is in flux. As to how this scenario is executed, I never asked.

Thank you for mentioning radiation reaction.

[swansont]

1 hour ago, DandelionTheory said:

I don't understand why we are not on the same page. I read the force on a charge is due to an applied external electric field and curved by an applied external magnetic field. No where does it say anything about lorentz forces due to the electrons own magnetic field.

A changing electric field creates a magnetic field. No electron involved. 

https://en.wikipedia.org/wiki/Maxwell's_equations#Formulation_in_SI_units_convention

[DandelionTheory]

1 hour ago, swansont said:

A changing electric field creates a magnetic field. No electron involved. 

https://en.wikipedia.org/wiki/Maxwell's_equations#Formulation_in_SI_units_convention

Thank you. This doesn't answer the issue. 

A fluctuating electric field changes the current within the loop and it's magnetic field, got it. Why is this an additional factor when calculating velocity of a charged particle in a constant magnetic field? Why is the other magnetic field in question when the changing variables do not effect that field magnitude?

[swansont]

27 minutes ago, DandelionTheory said:

Thank you. This doesn't answer the issue. 

Yes, actually, it does. 

Quote

A fluctuating electric field changes the current within the loop and it's magnetic field, got it. Why is this an additional factor when calculating velocity of a charged particle in a constant magnetic field? Why is the other magnetic field in question when the changing variables do not effect that field magnitude?

No, the fact that the field is changing inherently results in a magnetic field. Not because of a change in current. There need not be any loop, or current. In the 4th equation in the link (Ampere’s circuital law), when you set the current to zero, you still have the curl of B being proportional to the time rate of change of E

The changing field matters because it’s there, and changing. It does affect the field magnitude.

[joigus]

3 hours ago, DandelionTheory said:

I guess I need to wait for the edit window to expire. My apologies.

OK. Sorry on my part if I didn't understand or took some time to edit some of the answers.

Besides Swansont's very helpful assistance with the concepts, IMO, very much overlapping with mine --you'd better pay attention to him--, I see these other questions:

The situation you describe still has a lot of freedom. It does not determine the dynamics. To give you an idea of how many things it depends on:

1) The initial velocity of the electron

2) The geometry of the E(t) electric field

3) The way in which E(t) changes with time

4) The geometry and placement/orientation of the magnet

5) The fact whether magnet and sources of E(t) --example: charging or discharging capacitor plates-- can be considered as independent of each other

And finally you must apply the Lorentz force law on the electron (is the initial velocity of e^- parallel or perpendicular to field lines?, etc.)

I would advice you to draw a picture of what you have in mind.

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It must be understood that the effects of the electron on the rest of the setting are completely negligible.