P27_010.PDF

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10. (a) The current resulting from this non-uniform current density is
R
i
=
cylinder
J dA
=
0
J
0
1
−
r
1
1
2πrdr =
πR
2
J
0
=
AJ
0
.
R
3
3
(b) In this case,
J
0
i
=
J dA
=
R
cylinder
R
r
·
2πrdr =
0
2
2
2
πR J
0
=
AJ
0
.
3
3
The result is different from that in part (a) because the current density in part (b) is lower near the
center of the cylinder (where the area is smaller for the same radial interval) and higher outward,
resulting in a higher average current density over the cross section and consequently a greater
current than that in part (a).

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