Question about Magnetic induction of circular loop

[BREAD]

Homework Statement

Homework Equations

The Attempt at a Solution

This is what i did about (a)
but i don't know how to approach (b), it doesn't have x,y components, only Bz component.

 

[haruspex]

I think your answer to a is right - not expert in this area.
For b, a dependent variable being zero at some value of the independent variable does not imply that its derivative is also zero there.
I suggest working on b2, returning to b1 afterwards.

 

[BREAD]

I think i solve (1), but the problem is (2),(3)

 

[haruspex]

I think i solve (1)

And very neatly too.

the problem is (2),(3)

These are easy. Fundamental differential calculus: f(x+Δx)≈f(x)+f'(x)Δx.

 

[BREAD]

And very neatly too.

These are easy. Fundamental differential calculus: f(x+Δx)≈f(x)+f'(x)Δx.

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I tried it , but is (2) right? and idw how to get ∂(B_z)/∂y|_(0, 0, z). I heard somewhere that by properties of curl of B (as i wrote)
∂(B_z)/∂y|_(0, 0, z) is changed to ∂(B_y)/∂z|_(0, 0, z), but i can't solve this.

 

[haruspex]

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View attachment 114508

I tried it , but is (2) right? and idw how to get ∂(B_z)/∂y|_(0, 0, z). I heard somewhere that by properties of curl of B (as i wrote)
∂(B_z)/∂y|_(0, 0, z) is changed to ∂(B_y)/∂z|_(0, 0, z), but i can't solve this.

Isn't B_y identically zero on the z axis?