R Learning Goal To practice Problem-Solving Strategy 28.2 Ampere\'s Law Rank fro

Question

R Learning Goal To practice Problem-Solving Strategy 28.2 Ampere's Law Rank from largest to smallest. To rank items as equivalent, overlap them A solid cylindrical conductor is supported by insulating disks on the axis of a conducting tube with outer radius 7.15 cm and inner radius R 3.85 cm. Reset Help (Figure 1) The central conductor and the conducting tube carry equal currents of I = 4.05 A in opposite directions The currents are distributed uniformly over the cross Figure Largest Smallest Ra The correct ranking cannot be determined

Explanation / Answer

as per ampere’s law:

line integral of magnetic field =mu*current enclosed

where mu=magnetic permeability

for r=Rb:

current enclosed=I

if magnetic field is B, then

B*2*pi*Rb=mu*I

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

for r>Ra:

current enclosed=I-I=0

so magnetic field B=0

for r=Ra:

current enclosed=I-I=0

magnetic field=0

for Rb<r<Ra:

surface current density on the outer surface

=I/(pi*(Ra^2-Rb^2))

so current enclosed by a radial part of r=I1=*(pi*(r^2-Rb^2))/(pi*(Ra^2-Rb^2))

if magnetic field is B,

then B*2*pi*r=I-I1

==>B=(I-I1)/(2*pi*r)

as I1 <I, B is positive but less that field at r=Rb

hence the ranking will be:

field at Rb > (field at Rb<r<Ra) > (field at r=Ra) = (field at r>Ra)

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