# Electron enters magnetic field at 5000V -- What's the radius?

Hi! I'm getting ready for an exam and want to make sure if I solved some problems correctly. I would be grateful for your feedback 1. Homework Statement

After going through potential difference of 5000 V an electron falls in uniform magnetic field.
It’s induction is 0.1T and the electron’s speed is perpendicular to the lines of the magnetic field.
Find:
A. radius of the circle around which the electron will be moving
B. time it takes for the electron to travel one full circle.

## Homework Equations

K = eU = mv^2/2
F = mv^2/r = B*q*v

## The Attempt at a Solution

B = 0.1 T
U = 5000 V

Also if the electron is moving from left to right, and the magnetic field goes from top to bottom - Lorentz’s force would push it “into the screen”.

Since the kinetic energy of an electron K = eU = mv^2/2 we can find the speed.

e = 1.6*10^-19 J
m = 9.1*10^-31 kg

So v^2 = 2eU/m = (2*1.6*10^-19*5000)/(9.1*10^-31) = 1.75824176*10^15
v = sqrt(1.75824176*10^15) = 41931393.5 m/s

Because there’s centripetal magnetic force acting on the electron F = mv^2/r = B*q*v. Therefore r = mv/(B*q)
r = (9.1*10^-31*41931393.5)/(0.1*1.6*10^-19) = 2.38484801*10^-3 m
Or r = 2.38484801 mm.

To find the time we divide the length of the path by the speed, so
t = 2Pi*r/v = (2*3.14*2.38484801*10^-3)/41931393.5 = 3.57175001*10^-10 s

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## Answers and Replies

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TSny
Homework Helper
Gold Member
Also if the electron is moving from left to right, and the magnetic field goes from top to bottom - Lorentz’s force would push it “into the screen”.
Did you take into account that the electron carries a negative charge?

The rest of your work looks good. But you should never write so many digits in your numerical calculations. Only include significant figures.

• AlexPilk
Did you take into account that the electron carries a negative charge?

The rest of your work looks good. But you should never write so many digits in your numerical calculations. Only include significant figures.
Thank you :) If the charge is negative - then Lorentz force should act in the opposite direction (out of the screen)?

BiGyElLoWhAt
Gold Member
Dang that's quick. That electron is booking.

Assuming this is purely classical (non relativistic), it looks fine to me. I didn't check the actual numbers, but the procedure is correct.

• AlexPilk
Dang that's quick. That electron is booking.

Assuming this is purely classical (non relativistic), it looks fine to me. I didn't check the actual numbers, but the procedure is correct.
Thanks!

TSny
Homework Helper
Gold Member
If the charge is negative - then Lorentz force should act in the opposite direction (out of the screen)?
Yes.

Yes.
One more question, I just can't fully understand it. If you have a wire in a magnetic field with some current going through it - the direction of the force will be according to the left (or sometimes called right) hand rule. But it would be opposite for a single electron, right?
If current is a stream of electrons - why isn't the direction the same in those two cases?

BiGyElLoWhAt
Gold Member
Conventional current is taken in the direction a positive charge would flow. Ben Franklin got it wrong, originally, and we just stuck with it.

Conventional current is taken in the direction a positive charge would flow. Ben Franklin got it wrong, originally, and we just stuck with it.
You mean current is actually a flow of positively charged particles?

BiGyElLoWhAt
Gold Member
No, but when we write it down on paper, we choose the direction of the current to be the direction that would be taken by a positively charged particle, were that the case. We didn't know that electrons were actually what were causing electricity for a while, and we had no reason to assume that it was a negatively charged particle that was the one doing the moving around. We had a 50/50 shot, and we got it wrong lol.

No, but when we write it down on paper, we choose the direction of the current to be the direction that would be taken by a positively charged particle, were that the case. We didn't know that electrons were actually what were causing electricity for a while, and we had no reason to assume that it was a negatively charged particle that was the one doing the moving around. We had a 50/50 shot, and we got it wrong lol.
Oh, you mean electrons actually flow from - to + but we supposed stuff flows from + to - ?

BiGyElLoWhAt
Gold Member
Yes, and that's how it is taken on paper. It's called conventional current, and it is usually what is used. I say usually, but I haven't used real electron flow to analyze a circuit, ever. Any time there's a current, it's always been conventional.

• AlexPilk
Yes, and that's how it is taken on paper. It's called conventional current, and it is usually what is used. I say usually, but I haven't used real electron flow to analyze a circuit, ever. Any time there's a current, it's always been conventional. Haha, I didn't know this, it's fun :) But if a positively charged particle (like a proton) flies into a magnetic field - it's going to behave according to the left hand rule? I mean it would get pushed in the correct direction unlike an electron. What about a neutron? SInce it has no charge - what would be the direction of the force?

BiGyElLoWhAt
Gold Member
No, protons, or conventional current both obey the right hand rule.
Electrons would follow the left hand rule. Anything negatively charged, actually.

It is actually a really interesting story the way that my prof told it. I would guess that he embellished a little, however.

• AlexPilk
No, protons, or conventional current both obey the right hand rule.
Electrons would follow the left hand rule. Anything negatively charged, actually.

It is actually a really interesting story the way that my prof told it. I would guess that he embellished a little, however.
Thanks a lot :)