Calculating Magnetic Force on a Current-Carrying Wire

[fiyavan]

Hello guys

I have the following problem :

At a certain location, Earth has a magnetic field of 8.4 X 10^-5 T pointing 40 degree below the horizontal in a north-south plane. A 14.1m long straight wire carries a(n) 7 A current.
If the current is directed horizontally toward the east, what is the magnitude of the magnetic force on the wire?

I used the formula for the F = BIL sin Ө
so I get (8.4 X 10^-5 T)(7A)(14.1m) sin (40) = 0.0061775842N
for the magnetic force, but this is not the correct answer

Can anyone perhaps help me spot what am I doing wrong?

 

[Doc Al]

Your error is thinking that the angle between the direction of the current and the direction of the magnetic field is 40 degrees. (40 degrees is the angle that the field makes with the horizontal, but in a north-south plane.)

 

[fiyavan]

hmm

reading the problem again, it does seem like that's my problem, but I am still not quite understanding the wording of the problem, can you explain it to me please?

 

[Doc Al]

Here's how I visualize it: Take east to be the +x direction; north to be the +y direction. Below the horizontal means in the -z direction. The magnetic field vector is in the y-z plane. (What's the angle between the x-axis and the y-z plane?)

 

[itryphysics]

wouldnt it still be 10 degrees?