Optics Question 176

Question: A long straight wire of resistance R, radius a and length l carries a constant current I. The Poynting vector for the wire will be

Options:

A) $ \frac{IR}{2\pi al} $

B) $ \frac{IR^{2}}{al} $

C) $ \frac{I^{2}R}{al} $

D) $ \frac{I^{2}R}{2\pi al} $

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Answer:

Correct Answer: D

Solution:

Electric field $ E=\frac{v}{l}=\frac{iR}{l} $

(R = Resistance of wire) Magnetic field at the surface of wire $ B=\frac{{\mu _{0}}i}{2\pi a} $

(a = radius of wire) Hence poynting vector, directed radially inward is given by

$ S=\frac{EB}{{\mu _{0}}}=\frac{iR}{{\mu _{0}}l}.\frac{{\mu _{0}}i}{2\pi a}=\frac{i^{2}R}{2\pi al} $



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