If you are redistributing all or part of this book in a print format, ![]() Want to cite, share, or modify this book? This book uses the This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission. Because of the cylindrical symmetry, B → B → is constant along the path, and We determine the magnetic field between the conductors by applying Ampère’s law to the dashed circular path shown in Figure 14.11(b).The self-inductance per unit length is determined based on this result and Equation 14.22. After the integration is carried out, we have a closed-form solution for part (a). The magnetic energy is calculated by an integral of the magnetic energy density times the differential volume over the cylindrical shell. Based on this magnetic field, we can use Equation 14.22 to calculate the energy density of the magnetic field. The magnetic field both inside and outside the coaxial cable is determined by Ampère’s law. ![]() ![]() (c) The cylindrical shell is used to find the magnetic energy stored in a length l of the cable. (b) The magnetic field between the conductors can be found by applying Ampère’s law to the dashed path. Figure 14.11 (a) A coaxial cable is represented here by two hollow, concentric cylindrical conductors along which electric current flows in opposite directions.
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