please help A B C D E MasteringPhysics: Chapter 28 Assignment - Google Chrome Se

Question

please help A B C D E

MasteringPhysics: Chapter 28 Assignment - Google Chrome Secure https://session.masteringphysics.com/myct/item Chapter 28 Assignment Problem 28.78 Constants Along, straight solid cylinder, oriented with its axis in the z- direction carries a current whose current density is J The current density although symmetrical about the cylinder axis, is not constant and varies according to the relationship for a for a where the radius of the cylinder is a 5.00 em r is the radial distance from the cylinder axis, b is a constant equal to 600 A/m, and is a constant equal to 2.50 cm

Explanation / Answer

part A:

total current I0=integration of J*2*pi*r*dr

=2*pi*b*e^((r-a)/delta)*dr

from r=0 to r=a

=2*pi*b*e^((r-a)/delta)*delta

using limits from r=0 to r=a,

I0=2*pi*b*delta*(1-e^(-a/delta))

part B:

using the values, I0=81.493 A

part C:

using ampere’s law,

B*line integral of path=mu*total current enclosed

==>B*2*pi*r=mu*I

==>B=mu*I/(2*pi*r)

where mu=magnetic permeability

part D:

icurrent contained in a circular cross section of radius r =ntegration of J*2*pi*r*dr

=2*pi*b*e^((r-a)/delta)*dr

from r=0 ro r

=2*pi*b*e^((r-a)/delta)*delta

using limits,

I=2*pi*b*delta*(e^((r-a)/delta)-1)

using I0=2*pi*b*delta*(1-e^(-a/delta))

I/I0=(e^((r-a)/delta)-1)/(1-e^(-a/delta))

==>I=((e^((r-a)/delta)-1)/(1-e^(-a/delta)))*I0

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