In figure (top view of copper cylinders), a solid inner cylinder has uniform cross-section throughout its length. The radius of this cylinder, whose rotation axis is z-axis, is given as a = 5 cm. In high- frequency AC circuit, the current density of inner conductor can be modeled as being directly proportional only with p? that it depends neither z nor ¢ variable. This inner cylinder is concentric with a hollow cylindrical outer conductor of inner radius b=9 cm and outer radius c= 10 cm. Although due to high-frequency AC circuit, this outer conductor should have current density dependent on p variable. However, since the thickness of outer cylinder is small, in this question, it can be considered that only the outer cylinder (not the inner cylinder) has uniform current density. Both cylinders extending along z-axis have L = 5 m length, which can be assumed to be infinitely long. The plane of z = 0 passes through the middle points of these lengths. The medium except conductors is free-space. For inner conductor, total current of i = 1 mA flows along out of page direction. For outer conductor, total current of i2 = 2 mA flows along out of page direction. a) At z = 0 plane, what are the magnitudes of magnetic field intensity values at p = 4, 7, 9.5 cm and 15 cm? b) Consider three regions (Region I: p< a, Region II: a
In figure (top view of copper cylinders), a solid inner cylinder has uniform cross-section throughout its length. The radius of this cylinder, whose rotation axis is z-axis, is given as a = 5 cm. In high- frequency AC circuit, the current density of inner conductor can be modeled as being directly proportional only with p? that it depends neither z nor ¢ variable. This inner cylinder is concentric with a hollow cylindrical outer conductor of inner radius b=9 cm and outer radius c= 10 cm. Although due to high-frequency AC circuit, this outer conductor should have current density dependent on p variable. However, since the thickness of outer cylinder is small, in this question, it can be considered that only the outer cylinder (not the inner cylinder) has uniform current density. Both cylinders extending along z-axis have L = 5 m length, which can be assumed to be infinitely long. The plane of z = 0 passes through the middle points of these lengths. The medium except conductors is free-space. For inner conductor, total current of i = 1 mA flows along out of page direction. For outer conductor, total current of i2 = 2 mA flows along out of page direction. a) At z = 0 plane, what are the magnitudes of magnetic field intensity values at p = 4, 7, 9.5 cm and 15 cm? b) Consider three regions (Region I: p< a, Region II: a
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Transcribed Image Text:In figure (top view of copper cylinders), a solid inner cylinder has
uniform cross-section throughout its length. The radius of this
cylinder, whose rotation axis is z-axis, is given as a = 5 cm. In high-
frequency AC circuit, the current density of inner conductor can be
modeled as being directly proportional only with p? that it depends
neither z nor ¢ variable. This inner cylinder is concentric with a
hollow cylindrical outer conductor of inner radius b=9 cm and outer
radius c= 10 cm. Although due to high-frequency AC circuit, this outer conductor should have
current density dependent on p variable. However, since the thickness of outer cylinder is small,
in this question, it can be considered that only the outer cylinder (not the inner cylinder) has
uniform current density. Both cylinders extending along z-axis have L = 5 m length, which can
be assumed to be infinitely long. The plane of z = 0 passes through the middle points of these
lengths. The medium except conductors is free-space. For inner conductor, total current of i =
1 mA flows along out of page direction. For outer conductor, total current of i2 = 2 mA flows
along out of page direction.
a) At z = 0 plane, what are the magnitudes of magnetic field intensity values at p = 4, 7, 9.5 cm
and 15 cm?
b) Consider three regions (Region I: p< a, Region II: a<p<b, Region III: b<p<c). Assume
that you have calculated magnetic flux for each region (do not make any calculation to get
results). Compare the magnetic fluxes of these regions (greater? smaller? same?) with the ones
for DC case where the inner conductor has also uniform current density by keeping all other
parameters/values same given in the question. Make qualitative explanations, do not make any
quantitative calculations with numbers. If you want/need, you can
use symbolic
equations/calculations with symbols a, b, c, L, i1, i2, p, etc. to show your reasoning.
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