Heat development from wire bent into a circle
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The following quantities appear in the problem:
elektrische Stromstärke \(I\) / Magnetische Flussdichte \(B\) / elektrische Spannung \(U\) / Leistung \(P\) / elektrischer Widerstand \(R\) / Radius \(r\) /
The following formulas must be used to solve the exercise:
\(P = UI \quad \) \(B = \dfrac{\mu_0 I}{2r} \quad \) \(U=RI \quad \)
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Exercise:
A wire with RO electrical resistance is bent o a circle with rO radius. At what rate does the wire dissipate heat if one measures BO in its center?
Solution:
Geg R RO R r rO r B BO B GesPowerPsiW The enquoterate of heat dissipation is energy heat dissipation per time rate. So it corresponds to power. The current measured in the wire is: I frac r Bmu_ frac r Bncmu I So there is U RI R frac r Bmu_ R I U voltage applied to the wire and there will be P UI R frac r Bmu_ frac r Bmu_ R leftfrac r Bmu_right^ U I P approx PS heat dissipation. P R leftfrac r Bmu_right^ PS PP
A wire with RO electrical resistance is bent o a circle with rO radius. At what rate does the wire dissipate heat if one measures BO in its center?
Solution:
Geg R RO R r rO r B BO B GesPowerPsiW The enquoterate of heat dissipation is energy heat dissipation per time rate. So it corresponds to power. The current measured in the wire is: I frac r Bmu_ frac r Bncmu I So there is U RI R frac r Bmu_ R I U voltage applied to the wire and there will be P UI R frac r Bmu_ frac r Bmu_ R leftfrac r Bmu_right^ U I P approx PS heat dissipation. P R leftfrac r Bmu_right^ PS PP