Force of a wire induced by earth magnetic field

AI Thread Summary
The discussion revolves around calculating the magnetic force on a power cable carrying a current of 330 A in the Earth's magnetic field. The relevant formula is F = BILsinΘ, where the magnetic field strength is 5.0 x 10^-5 T and the angle of dip is 24°. There is confusion regarding the angle formed between the magnetic field and the current, with clarification that the magnetic field has both horizontal and vertical components. The correct interpretation indicates that the magnetic force acts at an angle of 66° above the horizontal towards the north. Understanding the orientation of the magnetic field components is crucial for solving the problem accurately.
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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.
27-p-075.gif

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!
 
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Hello.

Note that the current is toward the east.

How is this direction related to the direction of B?
 
Last edited:
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?
 
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.
 
Got it! Thank you so much.
 
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