Force of a wire induced by earth magnetic field

[R2D2]

Homework Statement

The power cable for an electric trolley (see figure) carries a horizontal current of 330 A toward the east. The Earth's magnetic field has a strength 5.0 ✕ 10-5 T and makes an angle of dip of24° at this location. Calculate the magnitude and direction of the magnetic force on a 20 m length of this cable.

Homework Equations

F=BILsinΘ

The Attempt at a Solution

I thought the question means there B and I form a 24° angle, so I tried F= 5.0 x 10^-5 x 20 x 330 x sin 24°. However, it seems that the answer is F=BILsin90, and the direction of the magnetic force is 66 above the horizontal towards the north. How can a magnetic force not perpendicular to the plane of B and I? I am really confused. Please help me here, thanks!

 

[TSny]

Hello.

Note that the current is toward the east.

How is this direction related to the direction of B?

 

[R2D2]

Thanks for your reply!

This is where I got confused.
So the current is toward east, and the direction of B is towards the northeast, and the angle is 24. So B and I form a angle of 66. - That's how I interpret the angle of dip. Is this wrong?

 

[TSny]

The B field is not northeast. The B field has a vertically downward component and a horizontal component (parallel to the ground). The horizontal component is toward the north. Looking at the picture, you are facing north as the current flows east. The B field has a horizontal component into the picture and also a vertical component from the top of the picture toward the bottom of the picture.

 

[R2D2]

Got it! Thank you so much.