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

• ChiralSuperfields
In summary: The magnetic flux is negative when the angle between the field lines and the surface normal is greater than 90 degrees.

#### ChiralSuperfields

Homework Statement
Relevant Equations
For the problem attached,
Why is the magnetic Flux not zero through the loop?

Many thanks!

#### Attachments

• Screenshot_20230130-113420_Chrome.jpg
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Here‘s a picture of the field lines. Why do you think the answer is zero?

ChiralSuperfields
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.

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.

ChiralSuperfields
The flux is a measure of the net amount going through a surface. What equation are you using for flux?

ChiralSuperfields
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 ##

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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ChiralSuperfields
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!

Yes it varies, but it is all the same sign. What is the sign?

ChiralSuperfields
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.

Frabjous