## Related questions with answers

A resistor consists of a solid cylinder of radius $r$ and length $L$. The resistor has resistance $R$ and is carrying current $i$. Use the Poynting vector to calculate the power radiated out of the surface of the resistor.

Solution

VerifiedWe will start with equation for power radiated from surface with surface area $A$ that is radiating electromagnetic waves with intensity $I$. Since intensity of Poynting vector is same as intensity of the electromagnetic waves $I=S$, we will plug in expression for Poynting vector into the equation for power radiated from surface. Then we will plug in expression for electric field inside the cylindrical conductor and expression for magnetic field of cylindrical conductor. Since electric field of the cylindrical conductor will be expressed in terms of voltage across cylindrical conductor, we will use Ohm's law to write voltage across cylindrical conductor in terms of given current through the cylindrical conductor and resistance of cylindrical conductor.

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