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

[AlexPilk]

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

 

[TSny]

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]

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]

If the charge is negative - then Lorentz force should act in the opposite direction (out of the screen)?

Yes.

 

[AlexPilk]

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]

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

 

[AlexPilk]

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]

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.

 

[AlexPilk]

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]

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]

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 :)