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A current I flows along a straight conductor with round cross-section. Find the flux of the Poynting vector across the lateral surface of the conductor's segment with resistance R. |
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Answer» Solution :Suppose the radius of the conductor is `R_(0)`. Then the conduction current density is `j_(c) = (I)/(piR_(0)^(2)) = sigmaE` or `E = (I)/(piR_(0)^(2)sigma) = (rhoI)/(piR_(0)^(2))` where `rho = (1)/(sigma)` is the resistivity. Inside the conductor there is a MAGNETIC field given by `H.2pi R_(0) = I` or `H = (I)/(2piR_(0))` at the edge LTBRGT `:.` Energy flowing in per second in a section of length `l`is `EH xx2piR_(0)l = (rhoI^(2)l)/(piR_(0)^(2))` But the resistance `R = (rhol)/(piR_(0)^(2))` Thus the energy flowing into the conductor `= I^(2)R`. |
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