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A coaxial cable has an inner conductor of radius a, and outer thin cylindrical shell of radius b. A steady current I flows in the inner conductor and returns in the outer conductor. Consider the following two cases, A and B, which describe how current is flowing though the structure. In case A the current in the inner conductor is distributed only on the surface. In case B the current in the inner cylinder is distributed uniformly over its cross-section. How does the amount of stored magnetic potential energy compare between cases A and B? Case B has more stored energy It is impossible to say without knowing how much bigger radius b is than radius a O Case A has more stored energy Case A and Case B have the same amount of stored energy

A coaxial cable has an inner conductor of radius a, and outer thin cylindrical shell of radius b. A steady current I flows in the inner conductor and returns in the outer conductor. Consider the following two cases, A and B, which describe how current is flowing though the structure. In case A the current in the inner conductor is distributed only on the surface. In case B the current in the inner cylinder is distributed uniformly over its cross-section. How does the amount of stored magnetic potential energy compare between cases A and B? Case B has more stored energy It is impossible to say without knowing how much bigger radius b is than radius a O Case A has more stored energy Case A and Case B have the same amount of stored energy

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**Understanding Stored Magnetic Energy in Coaxial Cables** A coaxial cable consists of an inner conductor with a radius \( a \) and an outer thin cylindrical shell with a radius \( b \). A steady current \( I \) flows through the inner conductor and returns through the outer conductor. This setup can be analyzed in two different cases, A and B, to examine how the current distribution affects the stored magnetic potential energy. **Case A:** The current in the inner conductor is distributed only on the surface. **Case B:** The current in the inner cylinder is uniformly distributed over its cross-section. **Question:** How does the amount of stored magnetic potential energy compare between cases A and B? The possible answers are: - \( \circ \) Case B has more stored energy - \( \circ \) It is impossible to say without knowing how much bigger radius \( b \) is than radius \( a \) - \( \circ \) Case A has more stored energy - \( \circ \) Case A and Case B have the same amount of stored energy Considerations need to be made regarding the magnetic field distribution and energy density in each configuration to determine the correct answer.
Transcribed Image Text:**Understanding Stored Magnetic Energy in Coaxial Cables** A coaxial cable consists of an inner conductor with a radius \( a \) and an outer thin cylindrical shell with a radius \( b \). A steady current \( I \) flows through the inner conductor and returns through the outer conductor. This setup can be analyzed in two different cases, A and B, to examine how the current distribution affects the stored magnetic potential energy. **Case A:** The current in the inner conductor is distributed only on the surface. **Case B:** The current in the inner cylinder is uniformly distributed over its cross-section. **Question:** How does the amount of stored magnetic potential energy compare between cases A and B? The possible answers are: - \( \circ \) Case B has more stored energy - \( \circ \) It is impossible to say without knowing how much bigger radius \( b \) is than radius \( a \) - \( \circ \) Case A has more stored energy - \( \circ \) Case A and Case B have the same amount of stored energy Considerations need to be made regarding the magnetic field distribution and energy density in each configuration to determine the correct answer.
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