Please, solution for a and b. Problem 5.4 in Jackson
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Please, solution for a and b. Problem 5.4 in Jackson
![5.4
A magnetic induction B in a current-free region in a uniform medium is cylindrically
symmetric with components B₂(p, z) and Bµ(p, z) and with a known B₂(0, z) on the
axis of symmetry. The magnitude of the axial field varies slowly in z.
apter 5 Magnetostatics, Faraday's Law, Quasi-Static Fields-SI
(a) Show that near the axis the axial and radial components of magnetic induction
are approximately
4)
№²B₂(0, z)
az2
+
3
- (9) [8.0.2)] + (²) [³B.0, 0]
aB₂(0, z)
№³B₂(0, z) +
əz
16
B₂(p, z)= B₂(0, z) -
B₂(p, z) =
(b) What are the magnitudes of the neglected terms, or equivalently what is the
criterion defining "near" the axis?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1bb380f6-534f-47ee-a8fc-d4cf03a07213%2Fd5c824cc-b0e2-4cbd-aa47-c51aa8ac5b71%2Fpqpnvhr_processed.png&w=3840&q=75)
Transcribed Image Text:5.4
A magnetic induction B in a current-free region in a uniform medium is cylindrically
symmetric with components B₂(p, z) and Bµ(p, z) and with a known B₂(0, z) on the
axis of symmetry. The magnitude of the axial field varies slowly in z.
apter 5 Magnetostatics, Faraday's Law, Quasi-Static Fields-SI
(a) Show that near the axis the axial and radial components of magnetic induction
are approximately
4)
№²B₂(0, z)
az2
+
3
- (9) [8.0.2)] + (²) [³B.0, 0]
aB₂(0, z)
№³B₂(0, z) +
əz
16
B₂(p, z)= B₂(0, z) -
B₂(p, z) =
(b) What are the magnitudes of the neglected terms, or equivalently what is the
criterion defining "near" the axis?
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