How Far Does a Proton Travel Above a Current-Carrying Wire?

[kiwikahuna]

Homework Statement

A long straight wire lies on a horizontal table and carries a current of 1.09 μA. A proton moves parallel to the wire (opposite the current) with a constant velocity of 12200 m/s at a distance d above the wire. The acceleration of gravity is 9.8 m/s2.
Determine this distance of d. You may ignore the magnetic field due to the Earth. Answer in units of cm.

Homework Equations

F = mg
F = qvB
B = (mu)* I / (2pi*r)

The Attempt at a Solution

I set mg = qvB and I solved for B.

After I found B, I plugged B into the equation B = (mu)* I / (2pi*r) to find r which I assume to be the distance that the question is asking for.

Here are the numbers I worked with:

(1.67e-27 kg) (9.81 m/s^2) = (1.602e-19 C)(12200 m/s) * (B)
B = 8.38e-12

To find r,

8.38 e-12 = [(4pi e-7)*(1.09e-6)] / [2pi * r]
I solved for r and found it to be 25.67 cm but this isn't the right answer. Could someone tell me what I did wrong?

 

[G01]

I think you just lost a decimal place somewhere. I'm getting an answer of 2.56cm with the same numbers. I think you did the work correctly, but made a computational error. Check your calculations again.

 

[kiwikahuna]

No I tried submitting 2.5667 as the answer and it's still wrong. I think I might have gotten the formula wrong?

 

[mgb_phys]

I couldn't see anything wrong with the formulae - that's why I didn't post.
You probably don't want to put 5 sig figures when you only know the proton mass and g to 3, could that be it?
I don't really have an intuition about twhat the answer should be - it's not a setup I encounter on a day-day basis.

 

[kiwikahuna]

Unfortunately that's not the problem. The online homework automatically accepts as many sig figs as you can give it. I don't know why this is wrong though. I was sure I had it.

-stressed------

 

[G01]

I still think you did the problem right, other than the decimal error. Are you sure it wants the answer in centimeters? Are you sure of the units you used in the finding the answer?

 

[kiwikahuna]

Yep, the problem says that the answer has to be in cm units.

Let me recheck my units...

(1.67e-27 kg) (9.81 m/s^2) = (1.602e-19 C)(12200 m/s) * (B)
B = 8.38e-12 Tesla

8.38 e-12 Tesla = [(4pi e-7)*(1.09e-6 A)] / [2pi * r]

Hmm...everything looks like they are in the right units. Any other suggestions?

 

[G01]

Any other suggestions?

I'm sorry, but I'm stumped. There may be something that we are all missing, or the answer could be wrong. I would talk with your instructor about this problem.

 

[kiwikahuna]

I don't know whether to laugh or cry.. Turns out I did do the problem right except my rounding was a little bit off. I tried submiting 2.6002 cm and the darn system considered that answer right. Thank you SO much for your help.

 

[mgb_phys]

That annoys me about automatic test systems.
Does the designer consider ( or even understand) number of significant figures.
Does it check for a range of answers or just do string match.
I'm sure there are systems out there that are checking if your answer matches to a floating point number!

 

[Gokul43201]

Homework Statement

A long straight wire lies on a horizontal table and carries a current of 1.09 μA. A proton moves parallel to the wire (opposite the current) with a constant velocity of 12200 m/s at a distance d above the wire. The acceleration of gravity is 9.8 m/s2.

g=9.8, not 9.81 m/s^2

Most online homework software accepts a fixed percentage error (typically 1%).