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Deriving Magnetic Fields

  • Thread starter jisbon
  • Start date
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Homework Statement
Derive magnetic field at a point p away generated by current carrying loop and line.
Homework Equations
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So I have managed to derive the magnetic field of a current carrying wire, however, I seem to have some enquiries on deriving the one for the loop. In the formula where ##\frac {ds * r} {r^2}##, I know that it will become ##ds sin \theta.## However compared to the theta in the wire, the theta that most derivations (I was searching for solutions) seems to be the angle at the point instead of the angle from the loop. Anyone can shine a light on this? Thanks
 

BvU

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Bit hard to decipher your question without a drawing. Can I assume you are looking at the field in a point on axis ?
most derivations
Utterly vague. Mention one or two explicitly.

Oh, and: ##\ dssin\theta\ ## looks ugly; at least use \sin : ##ds\sin\theta##
 

kuruman

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If you are considering the magnetic field due to a circular current loop at some point ##z## on the axis of the loop, there are two angles involved, one is the azimuthal angle (normally labeled ##\phi##) that locates element ##d\vec s## on the current loop and the second angle (normally labeled ##\theta##) is the angle between the field element ##d\vec B## and either the ##z##-axis or one of the horizontal axes (see image below). Are these the angles you mean respectively by "theta in the wire" and "the angle at the point"?

Loop.png
 

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