A uniformly wound toroidal segment contains N identical small turns of area A carrying current I. Their magnetic-moment directions are uniformly distributed from angle -α to +α about the bisector. What is the resultant magnetic-moment magnitude?
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Question

A uniformly wound toroidal segment contains N identical small turns of area A carrying current I. Their magnetic-moment directions are uniformly distributed from angle -α to +α about the bisector. What is the resultant magnetic-moment magnitude?

Options

G1 Physics · Accepted Answer

The turn density is N/(2α). Transverse components cancel. The bisector component is [NIA/(2α)]∫₋α^α cosθ dθ=NIA sinα/α.

A uniformly wound toroidal segment contains N identical small turns of area A carrying current I. Their magnetic-moment directions are uniformly distributed from angle −α to +α about the bisector. What is the resultant magnetic-moment magnitude?