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1) Adapting an old exam question: Consider a hollow cylindrical conductor of inner radius b and outer radius 2b, which is carrying current INTO the page. A cross-section of the conductor is shown here where the x region indicates the part carrying the current. The current is uniformly distributed throughout the x region, with current density j. a) What is the total current I carried by this structure, in terms of b, j, and other constants? {2b b) What is the magnitude and direction of the magnetic field at the following radial distances from the center of the conductor? ri for 0

1) Adapting an old exam question: Consider a hollow cylindrical conductor of inner radius b and outer radius 2b, which is carrying current INTO the page. A cross-section of the conductor is shown here where the x region indicates the part carrying the current. The current is uniformly distributed throughout the x region, with current density j. a) What is the total current I carried by this structure, in terms of b, j, and other constants? {2b b) What is the magnitude and direction of the magnetic field at the following radial distances from the center of the conductor? ri for 0

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1) Adapting an old exam question: Consider a hollow cylindrical conductor of inner radius b and outer radius 2b, which is carrying current INTO the page. A cross-section of the conductor is shown here where the x region indicates the part carrying the current. The current is uniformly distributed throughout the x region, with current density j. a) What is the total current I carried by this structure, in terms of b, j, and other {2b^ constants? b) What is the magnitude and direction of the magnetic field at the following radial distances from the center of the conductor? ri for 0<r;<b rii for b<rii<2b i) ii) iii) c) Instead of a uniform current density j, the conductor is now carrying a NONuniform current density given by jnon= jr/b, where r is the radial distance from the center of the conductor and j and b are constants as before. Now, what is the total current carried by this conductor? (An integral might be in order..) Is it greater or less than before? (You can answer this part, even without getting the first...) rji for 2b<rii
Transcribed Image Text:1) Adapting an old exam question: Consider a hollow cylindrical conductor of inner radius b and outer radius 2b, which is carrying current INTO the page. A cross-section of the conductor is shown here where the x region indicates the part carrying the current. The current is uniformly distributed throughout the x region, with current density j. a) What is the total current I carried by this structure, in terms of b, j, and other {2b^ constants? b) What is the magnitude and direction of the magnetic field at the following radial distances from the center of the conductor? ri for 0<r;<b rii for b<rii<2b i) ii) iii) c) Instead of a uniform current density j, the conductor is now carrying a NONuniform current density given by jnon= jr/b, where r is the radial distance from the center of the conductor and j and b are constants as before. Now, what is the total current carried by this conductor? (An integral might be in order..) Is it greater or less than before? (You can answer this part, even without getting the first...) rji for 2b<rii
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