# Electrons move, causing magnetic force, find v?

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1. Jun 13, 2017

### Helly123

1. The problem statement, all variables and given/known data

2. Relevant equations
f = q.v.B.sin tetha
I = q/t = v/R

3. The attempt at a solution
(1) q =a.b.n.v.t is it right?
(2) I = q/t = abnvt/t = abnv is it right?
(3)F = q.v.B is it right?
(4) ?
(5) ?

is it right?

2. Jun 13, 2017

### Staff: Mentor

Right so far.
What do you think about (4) and (5)?

3. Jun 13, 2017

### Helly123

4&5 can you give me clue?

4. Jun 13, 2017

### scottdave

nabvt gives you the number of electrons passing in a given amount of time, t. So nabv gives you the number of electrons per second. Each electron has a charge -q, so this must be multiplied to get the current (charge/time). Volts are Joules/Coulomb = Newton*meters/Coulomb, if that helps you on #4.
You can rearrange that so that Force = Volts*Coulomb / meter, then see if you can find what fits that. Once you have an expression for V, you should be able to find the last one.

5. Jun 13, 2017

### Helly123

4) Volts = joules/Coulomb
Volts = F/q
V=Bvq/q
V=Bv??

5) q=abnvt
I=q/t
I=abnv
n=I/abv
n=I/ab.V/B
n=IB/abV

What's wrong on this?

6. Jun 14, 2017

### Staff: Mentor

A force is not an energy.

7. Jun 14, 2017

### Helly123

I've looked at the link you gave me.

8. Jun 14, 2017

### Helly123

V = joule (energy)/coulombs --- which is the energy?
joule can be force * distance
V = force * distance / coulombs
which is the distance?

9. Jun 14, 2017

### Staff: Mentor

In which direction does the force (calculated in 3) go? What is the corresponding distance where the voltage difference appears?

10. Jun 14, 2017

### scottdave

Using the right hand rule, in which direction is the force acting on the electrons (from F = qv x B)? Since work is the dot product of Force and the distance traveled, I think you should look for the distance in the same direction done. This is an interesting problem. I have not seen some of these terms expressed like this, but it gets you to thinking about how things are related.

11. Jun 14, 2017

### Helly123

I understand.
4) Voltage = Joules/C = force*distance / coulombs
V = f . distance / q
V= B*v*q . b / q
V = B*v . b
distance found by right hand rule, F go trough width which is b.

5) q = abnvt
n = q/abvt I=q/t
n = I/abv V = B*v*b --> v = V/Bb
n = I / (ab)V/Bb
n = IBb/abV
n = IB/aV ---> but answer is still wrong.. which is wrong?

12. Jun 14, 2017

### Staff: Mentor

Right.
It is useful to put brackets around denominators: n=q/(abvt). Otherwise you could misinterpret it as $n=\frac q a bvt$.
Right.
Why do you think it is wrong?

13. Jun 14, 2017

### Helly123

why... you sure it's right?

14. Jun 14, 2017

### Staff: Mentor

If you replace n by $\frac 1 {A_H}$, it is the usual formula for the Hall effect. The Hall constant as inverse electron density takes into account that not all electrons contribute to current flow.

15. Jun 14, 2017

### Helly123

I meant, the key answer is n = BI/aqV... but I don't think the key answer is wrong.

16. Jun 14, 2017

### Staff: Mentor

Ah, n is the electrons per volume, not the charge density. Then you need the factor q in the answer (this also applies to question 2).
In that case your notation for q is a bit strange.
q in the problem statement is a charge. What you calculate here is a number.

17. Jun 15, 2017

### Helly123

i still don't get it. What is n stands for? And n actually what? And my answer for 1 and 2 are they right?

18. Jun 15, 2017

### Staff: Mentor

n is something like "5/m3" (just with a larger number for actual materials) - the density of electrons.

qn is something like "5C/m3" - a charge density.
1 is right, 2 needs an additional factor q.

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