Magnetic Fields and Maximum Current

[Mehta29]

Hey guys I'm new here and needless to say I am completely lost...

well here is the problem...

What is the maximum current that a wire can carry if an experimenter is performing an experiment 0.60 m away that deals with the Earth's magnetic field (4.5*10-5 T), which she wishes to measure to +/- 1 percent?

i thought I could just plug the #'s given into

B = (4pi*10^-7)I / (2(pi)R)

and i ended up with 135 A...which seemed muuuuuuuuch too high...and assumably was wrong...

(4.5*10^-5) = (4pi*10^-7)I / 2(pi)(.6??)

It would be greatly appreciated if i could get this help tonight...but I just want to understand what I'm doing wrong for the most part...

 

[Mehta29]

well i found the error of my ways...

the whole +/- 1% threw me off...

i get the right answer if i multiply by the magnetic field by 1% and then re-plug everything in...

hopefully this helps someone in the future...

 

[kyle8921]

Hello and welcome! It seems like you are on the right track with using the equation B = (4pi*10^-7)I / (2(pi)R) to solve this problem. However, there are a few things to consider in order to get the correct answer.

First, let's look at the units. The Earth's magnetic field strength is given in Tesla (T), while the value of 4pi*10^-7 is in units of Tesla per meter (T/m). In order for the units to cancel out and leave you with the unit of current (A), you will need to multiply the value of 4pi*10^-7 by the distance (0.60 m) in meters. This will give you a value of 0.000000113 Tm.

Next, we need to rearrange the equation to solve for current (I). This can be done by multiplying both sides by 2(pi)R and dividing by the magnetic field strength (B). This will give us the equation I = (B*2(pi)R) / (4pi*10^-7).

Now, let's plug in the values given in the problem: B = 4.5*10^-5 T, R = 0.60 m. This gives us a value of 0.000135 A, or 135 mA. This is a much more reasonable value for the maximum current that the wire can carry in this experiment.

Finally, to account for the +/- 1 percent uncertainty, we can multiply the calculated value by 1.01 to get a range of 0.00013635 A to 0.00013365 A, or 136.35 mA to 133.65 mA.

I hope this helps you understand the problem better and get to the correct answer. Keep up the good work!