Magnetic Field of A Straight Conductor

In summary, the problem involves two hikers trying to read a compass under an overhead transmission line with a current of 400 Amps. The task is to find the magnitude and direction of the magnetic field at a point on the ground directly under the conductor. To solve this, the formula for a magnetic field of a straight wire is used, resulting in a magnetic field of 1.60x10^-5 Teslas going into the plane of the paper. For the second part, one hiker suggests walking another 50 meters to avoid inaccurate compass readings. It is determined that the Earth's magnetic field is much larger than that of the conductor, so it is not a significant problem for the compass readings. There is a mathematical way
  • #1
shikagami
42
0
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?
 
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  • #2
shikagami said:
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.
 
  • #3
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
 

Related to Magnetic Field of A Straight Conductor

1. What is a "magnetic field"?

A magnetic field is a region in space where a magnetic force can be detected. It is produced by moving electric charges and can exert a force on other moving electric charges.

2. How is a magnetic field created by a straight conductor?

A magnetic field is created around a straight conductor when an electric current flows through it. The strength of the magnetic field is directly proportional to the amount of current flowing through the conductor.

3. How does the direction of the magnetic field relate to the direction of the current in the conductor?

The direction of the magnetic field around a straight conductor is perpendicular to the direction of the electric current flowing through it. This means that if the current is flowing upwards, the magnetic field will form a circle around the conductor in a clockwise direction.

4. How does the strength of the magnetic field change with distance from the conductor?

The strength of the magnetic field decreases as the distance from the conductor increases. This is because the magnetic field lines spread out as they move away from the conductor, resulting in a weaker field at a greater distance.

5. What is the unit of measurement for magnetic field strength?

The unit for magnetic field strength is the tesla (T). It is a measure of the force exerted on a charged particle moving through the field at a certain velocity. Another common unit is the gauss (G), with 1 T = 10,000 G.

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