Question about Magnetic induction of circular loop

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Homework Help Overview

The discussion revolves around a problem related to magnetic induction in a circular loop, specifically focusing on the components of the magnetic field and their derivatives. Participants are exploring the implications of certain conditions and mathematical relationships in the context of magnetic fields.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss their attempts at solving parts of the problem, particularly focusing on the implications of having a zero component in the magnetic field and how that relates to derivatives. There is a mention of using properties of the curl of the magnetic field to relate different components.

Discussion Status

Some participants express confidence in their solutions to the first part of the problem but indicate uncertainty regarding subsequent parts. There is a mix of suggestions for revisiting earlier parts of the problem and exploring different mathematical approaches. The discussion reflects a collaborative effort to clarify concepts without reaching a definitive conclusion.

Contextual Notes

Participants are grappling with the implications of certain variables being zero and the relationships between different components of the magnetic field. There is mention of potential assumptions regarding the behavior of the magnetic field on the z-axis, which remains under discussion.

BREAD
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Homework Statement


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Homework Equations

The Attempt at a Solution


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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.
 
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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.
 
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I think i solve (1), but the problem is (2),(3)
 
BREAD said:
I think i solve (1)
And very neatly too.
BREAD said:
the problem is (2),(3)
These are easy. Fundamental differential calculus: f(x+Δx)≈f(x)+f'(x)Δx.
 
haruspex said:
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.
 
BREAD said:
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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 By identically zero on the z axis?
 

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