Magnetic Field of A Straight Conductor

[shikagami]

Here is a problem that I don't quite understand.

P: Two hikers are reading a compass under an overhead transmission line that is 5.0 meters above the ground and carries a current of 400 Amps in a direction from south to north.

a. Find the magnitude and direction of the magnetic field at a point on the ground directly under the conductor.

b. One hiker suggests they walk on another 50 meters to avoid inaccurate compass readings caused by the current. Considering that the magnitude of the Earth's field is of the order of 0.5 x 10^-4 Teslas, is the current really a problem?

Here is how I did it:

For part A I figured I should find the permeability by the formula (k'=Mo/4pi). After finding Mo (1.26x10^-6 N/A^2), I used the formula for a magnetic field of a straight wire [B=(MoI)/(2 (pi) r)]. I got 1.60x10^-5 Teslas for the magnetic field going into the plane of the paper.

For part B I said that since the Earth's magnitude is much bigger than that of the conductor that the conductor will not cause a significant problem to the accuracy of the compass readings.

Are any of my solutions right? Is there a mathematical way to prove part B?

 

[Gokul43201]

Here is a problem that I don't quite understand.

P: Two hikers are reading a compass under an overhead transmission line that is 5.0 meters above the ground and carries a current of 400 Amps in a direction from south to north.

a. Find the magnitude and direction of the magnetic field at a point on the ground directly under the conductor.

b. One hiker suggests they walk on another 50 meters to avoid inaccurate compass readings caused by the current. Considering that the magnitude of the Earth's field is of the order of 0.5 x 10^-4 Teslas, is the current really a problem?

Here is how I did it:

For part A I figured I should find the permeability by the formula (k'=Mo/4pi). After finding Mo (1.26x10^-6 N/A^2), I used the formula for a magnetic field of a straight wire [B=(MoI)/(2 (pi) r)]. I got 1.60x10^-5 Teslas for the magnetic field going into the plane of the paper.

i see nothing about a sheet of paper in the problem.

For part B I said that since the Earth's magnitude is much bigger than that of the conductor that the conductor will not cause a significant problem to the accuracy of the compass readings.

Are any of my solutions right? Is there a mathematical way to prove part B?

The mathematical way to handle part B, is to find the resultant field vector, and find its angle. This angle will tell you how wrong the hikers may have gotten.

 

[GCT]

P: Two hikers are reading a compass under an overhead transmission line that is 5.0 meters above the ground and carries a current of 400 Amps in a direction from south to north.

a. Find the magnitude and direction of the magnetic field at a point on the ground directly under the conductor.

The current have a magnetic field associated with it, try finding the proper formula. What will the unit vector be? You'll probably need to also consider the magnitude and direction of the Earth's magnetic field

for b, you'll need to find the new r value

feel free to ask further questions