# Charge carrier drift velocity of wire

1. Jan 16, 2017

### ravsterphysics

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

2. Relevant equations

3. The attempt at a solution

Current is I = nqvA so drift velocity V is: V = I/nqA

Drift velocity for x is: Vx = I/nqA

Drift velocity for y is: Vy = 2I/nqA

So the ratio of Vx : Vy should be 2:1 since Vy is equal to 2 lots of Vx?? (but correct answer is B)

2. Jan 16, 2017

### Staff: Mentor

You may want to rethink your logic there.

Edit: My mistake. I presumed that their table presented the ratios as $V_y:V_x$, but looking again at the text I see that it's the other way around. So the book's suggested answer is incorrect as you found.

Edit2: I retract my retraction! See later postings.

Last edited: Jan 16, 2017
3. Jan 16, 2017

### nickyfernandezzz

Nothing seems wrong with your calculation. Answer should be 2:1. But books sometimes give wrong answers.

4. Jan 16, 2017

### ravsterphysics

I've done this question a few times now and ended up with the same answer, but the question is from an official exam paper in the UK so I don't believe there's been a mistake.

FYI, here's what the mark scheme says:

How can it still be B?

5. Jan 16, 2017

### Staff: Mentor

I'm retracting my edit from before. Clearly the coffee isn't working this morning

If the cross sectional area is halved the velocity doubles. So Vy is twice Vx as you originally pointed out:
So $V_y$ is twice the size of $V_x$. That makes the ratio $V_x:V_y = 1:2$ which is indeed answer B.

6. Jan 16, 2017

### nickyfernandezzz

Indeed. Vy/2=Vx , so Vx: Vy should be 1:2 because then Vy÷2=1.

7. Jan 16, 2017

### ravsterphysics

Vx = I/nqA

and

Vy = 2[I/nqA] = 2Vx

so doesn't that mean that for every 1 part of Vx we have half a part of Vy? So that 2 parts of Vx gives 1 part of Vy so the ratio is still C, 2:1?? Argh!

8. Jan 16, 2017

### Staff: Mentor

Pick a value for the magnitude of Vx, say 1. What value would you assign to Vy using your expressions?

9. Jan 16, 2017

### nickyfernandezzz

2Vx=Vy. So , if the value of Vx is 1, value of Vy should be 2 right?

10. Jan 16, 2017

### Staff: Mentor

Right. So, Vx = 1, Vy = 2. What's Vx:Vy?

11. Jan 16, 2017

### nickyfernandezzz

Then Vx:Vy should be 1:2