Calculating magnetic force on circular coil carrying current

  • Thread starter cseil
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  • #1
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Homework Statement


A circular coil with center on the z axis and orthogonal to the xy axis carries a current. The coil is in a magnetic field B with axial simmetry compared to the x axis. B forms an angle θ with the z axis. Calculate the magnetic force acting on the coil.

exerc.png


2. Homework Equations

$$\vec{F_B} = i \vec{dl} x \vec{B}$$

The Attempt at a Solution


[/B]
I tried considering $$ dl = r d\phi $$
So [itex]F = irB_zd\phi [/itex]
where Bz is [itex]Bcos\theta[/itex]

By is null because it has opposite verse on opposite points of the coil. So I can consider just Bz

$$ F = irBcos\theta d\phi = irBcos\theta \int_0^{2\pi} d\phi = 2\pi irBcos\theta$$

The result, according to the book, is [itex]2\pi irBsin\theta[/itex]
Why?
 

Answers and Replies

  • #2
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How does your book define ##\theta##? Is it the angle the magnetic field makes with the horizontal(i.e. ##B_y##)?
 
  • #3
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How does your book define ##\theta##? Is it the angle the magnetic field makes with the horizontal(i.e. ##B_y##)?

It is the angle between B and Bz!
 
  • #4
rude man
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The coil is in a magnetic field B with axial simmetry compared to the x axis.
What does this mean?
 
  • #5
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What does this mean?

I can't understand what does it mean, actually.
 
  • #6
rude man
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I can't understand what does it mean, actually.
So ask! The problem is not you, it's the instructor who can't write understandably!
 

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