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

[member 731016]

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!

 

[Frabjous]

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

 

[member 731016]

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.

 

[nasu]

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.

 

[Frabjous]

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

 

[member 731016]

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 $\phi = BA\cos\theta$

 

[Frabjous]

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.

 

[member 731016]

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!

 

[Frabjous]

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

 

[member 731016]

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.