A coaxial cable has an inner conductor of radius a, and outer thin cylindrical shell of radius b. A current I flows in the inner conductor and returns in the outer conductor. The self-inductance of the structure will depend on bow the current in the inner cylinder tends to be distributed. Investigate the following two extreme cases. (a) Let current in the inner conductor be distributed only on the surface and find the self-inductance. (b) Let current in the inner cylinder be distributed uniformly over its cross-section and find the self-inductance. Compare with your results in (a).
A coaxial cable has an inner conductor of radius a, and outer thin cylindrical shell of radius b. A current I flows in the inner conductor and returns in the outer conductor. The self-inductance of the structure will depend on bow the current in the inner cylinder tends to be distributed. Investigate the following two extreme cases. (a) Let current in the inner conductor be distributed only on the surface and find the self-inductance. (b) Let current in the inner cylinder be distributed uniformly over its cross-section and find the self-inductance. Compare with your results in (a).
A coaxial cable has an inner conductor of radius a, and outer thin cylindrical shell of radius b. A current I flows in the inner conductor and returns in the outer conductor. The self-inductance of the structure will depend on bow the current in the inner cylinder tends to be distributed. Investigate the following two extreme cases. (a) Let current in the inner conductor be distributed only on the surface and find the self-inductance. (b) Let current in the inner cylinder be distributed uniformly over its cross-section and find the self-inductance. Compare with your results in (a).
Two identical long wires of radius a =1.53 mm are parallel and carry identical currents in opposite directions.Their center-to-center separation is d = 14.2 cm. Neglect the flux within the wires but consider the flux in the region between the wires.What is the inductance per unit length of the wires?
A solenoid used in magnetic resonance imaging ("MRI") has to be large enough for a human being to fit inside the solenoid cylinder, where there is a strong, uniform magnetic field produced. One such solenoid is wound from lots of adjacent turns of a single layer of (niobium-titanium) superconducting wire 2mm in diameter. Using the approximate size of a human, estimate relevant parameters about the solenoid, and use them to estimate the self-inductance of this solenoid.
Consider the rectangular loop in the figure below, which is fixed and under the influence of a uniform time-dependent magnetic field B (t). Show that the potential difference e (epsilon) induced in the loop is given by e = Acosθ db / dt, where A is the area of the loop.
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