Force of Earth's magnetic field acting on a power line?

[ted182]

Homework Statement

Imagine a power line carrying 1400A through the Earth's magnetic field in each of the following directions. Per meter, what is the magnitude of the force acting on the line:
A. to the North?
B. to the West?
C. in a direction that points 30 degrees south of west?

Homework Equations

and τ= B · I · L(1/2)W · sinθ (magnetic moment)

The Attempt at a Solution

First off, I need to say that this is all the information supplied. Looking back in my lesson (Apex online learning AP Physics), I found one mention to the Earth's magnetic field as being 4· 10^-5 T, so I have to assume they want me to use this. No dimensions of the line are given, so my idea to find the magnetic moment sounds like it won't work. My other equation above is to calculate the field around the wire, but I would still need "r," the distance to the wire which is not specified. My only other though is that the force will be zero when the line is parallel to the Earth's magnetic field. I immediately assumed this would be when the line is running north, but now I am wondering if it could be west (which way does the Earth's field actually "run?"). So, I am stuck. The lack of useful equations and information I have been provided with makes it seem like the answer is perhaps easier to find than I believe, but I have no idea. Any thoughts?

 

[rl.bhat]

Force on a current carrying wire is given by F = BILsin(theta) where theta is the angle between the current and the field.
Your answer for A is correct.
In B the current is perpendicular to the field.
And in C the angle is 120 degrees.

 

[nlightner]

Thank you for providing the context and your thoughts on this problem. I would approach this problem by first determining the direction of the Earth's magnetic field in the given scenario. Assuming the power line is located on the Earth's surface, the magnetic field would be directed towards the geographic North pole and would be considered as a vertical field.

Using the equation τ= B · I · L(1/2)W · sinθ, we can calculate the torque acting on the power line due to the Earth's magnetic field. Since the magnetic moment is not given, we can assume that it is proportional to the current (1400A) and the length of the power line.

A. To the North: In this scenario, the angle θ between the direction of the magnetic field and the power line is 0°, therefore the torque would be zero. This is because the sinθ term becomes zero.

B. To the West: In this scenario, the angle θ between the direction of the magnetic field and the power line is 90°, therefore the torque would be maximum. We can calculate the magnetic moment using the given current and length of the power line, and then use the equation τ= B · I · L(1/2)W · sinθ to find the magnitude of the torque acting on the power line.

C. In a direction that points 30 degrees south of west: In this scenario, the angle θ between the direction of the magnetic field and the power line would be 120°. Using the same approach as in part B, we can calculate the magnetic moment and then use the equation τ= B · I · L(1/2)W · sinθ to find the magnitude of the torque acting on the power line.

In conclusion, the magnitude of the force acting on the power line would depend on the direction of the line with respect to the Earth's magnetic field. The force would be maximum when the line is perpendicular to the magnetic field, and zero when the line is parallel to the magnetic field. I hope this helps!