Solved: A cylindrical resistor of length L, radius a, and resistance R carries current

Chapter 29, Problem 60

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A cylindrical resistor of length L, radius a, and resistance R carries current I. Calculate the electric and magnetic fields at the surface of the resistor, assuming the electric field is uniform over the surface. Calculate the Poynting vector and show that it points into the resistor. Calculate the flux of the Poynting vector (that is, 1 S S# dA S ) over the resistors surface to get the rate of electromagnetic energy flow into the resistor, and show that the result is I 2 R. Your result shows that the energy heating the resistor comes from the fields surrounding it. These fields are sustained by the source of electric energy that drives the current.