Flux from magnet (Why is the Flux not zero through the loop?)

In summary: The magnetic flux is negative when the angle between the field lines and the surface normal is greater than 90 degrees.
  • #1
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Homework Statement
Please see below
Relevant Equations
Please see below
For the problem attached,
Why is the magnetic Flux not zero through the loop?

Many thanks!
 

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  • #2
Here‘s a picture of the field lines. Why do you think the answer is zero?

B83565E0-E2F4-482B-B28D-55F536A61AB4.gif
 
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  • #3
Frabjous said:
Here‘s a picture of the field lines. Why do you think the answer is zero?

View attachment 321439
Thanks for your reply @Frabjous! because the number of field lines going into the loop is equal to the number going out.
 
  • #4
This is an open surface. There is no in and out. These apply only to closed surfaces. You should review the definition of flux through a surface. According to your idea, the flux would be always zero.
 
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  • #5
The flux is a measure of the net amount going through a surface. What equation are you using for flux?
 
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  • #6
Frabjous said:
The flux is a measure of the net amount going through a surface. What equation are you using for flux?
Thank you for your replies @nasu and @Frabjous ! The equation for magnetic flux is ##\phi = BA\cos\theta ##
 
  • #7
What is the sign of cosθ for the surface of interest? Hint: the normal to the surface is pointing to the right. The B field is pointing to the left.
 
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  • #8
Frabjous said:
What is the sign of cosθ for the surface of interest? Hint: the normal to the surface is pointing to the right. The B field is pointing to the left.
Thanks for your reply @Frabjous ! I think the direction of the B-field relative to the surface normal varies along the surface.

Many thanks!
 
  • #9
Yes it varies, but it is all the same sign. What is the sign?
 
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  • #10
Frabjous said:
Yes it varies, but it is all the same sign. What is the sign?
Thanks for your reply @Frabjous ! I think the sign is negative because ##\theta > 90 ## so ##\cos\theta < 0 ##

Thanks again, I see why the magnetic flux is negative now.
 
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