Question

A cylindrical conductor with a circular cross section has a radius q and a resistivity pand carries a constant current I (Take the current to be coming out of the page when the cross-sectional view of the conductor is in the plane of the page.) Part E What is the magnitude of the Poynting vector S at the same point? Express your answer in terms of the variables I. p. and appropriate constant ( ty and Submit Previour Answers Correct Part F What is the direction of this Poynting vector S? (The direction of Sis the direction in which electromagnetic energy flows into or out of the conductor) radially outwaard radially inward in the direction of the current opposite to the direction of the current Sub Previous Answers Correct Part G of the conductor. (Hint: Integrate Sover the surface of this volume.) Use the results in parts (e) and (t) to find the rate of flow of energy into the volume occupied by a length Express your answer in terms of the variables I. p. I. and appropriate constants (M. 6, and 90 AXPO I ? P- Submit Previour Answert Request Answer X Incorrect; Try Again; 4 attempts remaining - Part 1 Compare your result to the rate of generation of thermal energy in the same volume. %0AXRO? P/PR Submit Request Answer

Answer 1

Part G

Since S is constant over the surface of the conductor, the rate of energy flow P is given as :

P = SA

P = S * 2$\pi$aL

put value of S which you found in part (E)

P = ( $\rho$ I² / 2$\pi$²a³ ) 2$\pi$aL

P = $\rho$ LI² / $\pi$ a²

( NOTE - I have used capital L to prevent any confusion between I and L )

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Part H

from G,

P can also be written as

P = I²R

and

energy dissipated is also given as

P_R = I² R

so,

P / P_R = 1