Finding the direction of current given a varying magnetic....

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SUMMARY

The discussion centers on applying Ampere's Law, specifically the equation μ0 In,e = ∫B⋅ds, to determine the direction of current in a varying magnetic field. It is established that the integration should always be performed counterclockwise (CCW) around the loop, regardless of whether the magnetic field is increasing or decreasing. A positive result from the integral indicates that the current is directed out of the page, while a negative result indicates the current points into the page. This understanding is crucial for correctly interpreting the implications of magnetic field variations on current direction.

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  • Understanding of Ampere's Law and its integral form
  • Familiarity with magnetic fields and their properties
  • Knowledge of vector calculus, particularly line integrals
  • Basic concepts of Maxwell's equations
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alexdr5398
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Homework Statement


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Homework Equations


μ0 In,e = ∫B⋅ds

The Attempt at a Solution


I really don't how to approach this question at all.

Do you have to integrate counterclockwise around the loop every time? If the field was decreasing as y decreased, would you integrate CW or is it still CCW?

Why does μ0 In,e = ∫B⋅ds being >0 mean that it must be out of the page.
 
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The direction of ##\vec {ds}## has a meaning. You go around in a mathematically positive direction (CCW).

Ampere's law is an integral form of one of the maxwelll equations.

If ##d\vec l## in the link (your ##\vec {ds}## ) goes around CCW then ##\vec {d\bf {S}}## is pointing towards you (the positive z direction).

If the field is decreasing you still go around CCW and you get a negative ##\vec I## -- i.e. pointing in the negative z direction.
 
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BvU said:
The direction of ##\vec {ds}## has a meaning. You go around in a mathematically positive direction (CCW).

Ampere's law is an integral form of one of the maxwelll equations.

If ##d\vec l## in the link (your ##\vec {ds}## ) goes around CCW then ##\vec {d\bf {S}}## is pointing towards you (the positive z direction).

If the field is decreasing you still go around CCW and you get a negative ##\vec I## -- i.e. pointing in the negative z direction.

Okay, I understand. Thank you.
 

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