# Magnetic Force on a Power line

#### Dopefish1337

1. Homework Statement

A high-voltage power line carries a current of 106 A at a location where the Earth's magnetic field has a magnitude of 57.1 µT and points north, 71.9° below the horizontal. Calculate the magnitude of the magnetic force exerted on a 251 m length of wire if the current in the wire flows horizontally east.

2. Homework Equations

F=I*L*B*sin(theta) (magnitudes)

3. The Attempt at a Solution

106*251*57.1*10-6*sin(18.1)= 0.47198 N

However, the system says I'm wrong. Is the computer at fault here?

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#### LowlyPion

Homework Helper
1. Homework Statement

A high-voltage power line carries a current of 106 A at a location where the Earth's magnetic field has a magnitude of 57.1 µT and points north, 71.9° below the horizontal. Calculate the magnitude of the magnetic force exerted on a 251 m length of wire if the current in the wire flows horizontally east.

2. Homework Equations

F=I*L*B*sin(theta) (magnitudes)

3. The Attempt at a Solution

106*251*57.1*10-6*sin(18.1)= 0.47198 N

However, the system says I'm wrong. Is the computer at fault here?
I'd take a closer look at the angle. The power line is east west. The magnetic field lines are north south aren't they?

#### Dopefish1337

As far as I can tell, the field lines aren't exactly north south, hence the 71.9 degrees below horizontal. The field lines would then be angled sortof like "\", with direction being towards the upper end, versus the current in the wire shaped like "-" with the current going right(east). The angle between them looks like it would be 90+18.1=108.1 degrees.

However, using that angle, the resultant answer is 1.44 N, which is also incorrect. However, that was the correct answer to an otherwise identical question except where the current flowed directly south, which is where I figured I should be able to just subtract 90 degrees to get the new answer, hence my use of 18.1 degrees earlier.

#### LowlyPion

Homework Helper
As far as I can tell, the field lines aren't exactly north south, hence the 71.9 degrees below horizontal. The field lines would then be angled sortof like "\", with direction being towards the upper end, versus the current in the wire shaped like "-" with the current going right(east). The angle between them looks like it would be 90+18.1=108.1 degrees.

However, using that angle, the resultant answer is 1.44 N, which is also incorrect. However, that was the correct answer to an otherwise identical question except where the current flowed directly south, which is where I figured I should be able to just subtract 90 degrees to get the new answer, hence my use of 18.1 degrees earlier.
I understand the angle with the horizontal, but that is up and down. Which direction are the magnetic field lines directed in the N-S-E-W plane? Given that Earth has a North pole and South Pole wouldn't you think that N-S is the direction of the lines, in addition of course at that locale that it is 71.9° with the horizontal?

#### Dopefish1337

Well yes...Does this suggest that the angle given is unneeded for this question?

#### LowlyPion

Homework Helper
Well yes...Does this suggest that the angle given is unneeded for this question?
What is the direction of v then? E-W? And B is N-S? So ...

Now when you do your q*v X B, you will get a vector for the Lorentz force that is directed normal to the B field and that means you need the angle it makes with the horizon to determine direction, but isn't the question what is the |F|?

#### Dopefish1337

Thanks, got it now.

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