(a) Explanation Given Info: The current density is, J = { 2 I 0 π a 2 [ 1 − ( r a ) 2 ] k ^ for r ≤ a 0 for r ≥ a (I) Consider a small element in the form of a ring of area dA . Write the expression for the current. d I = J d A dI is the current through the element J is the current density The area of the small element in the form of the ring is, d A = ( 2 π r ) d r r is the radius of the ring dr is the width Replace dA by ( 2 π r ) d r in the expression for the current. d I = J ( 2 π r ) d r (II) Substitute Equation (I) in (II) (b) To determine The magnetic field in the region r ≥ a . (c) To determine The current contained in the cross section of the wire for r ≥ a . (d) To determine The magnetic field in the region r ≤ a .

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ISBN: 9781269542661

Author: YOUNG

Publisher: PEARSON C

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Question

Chapter 28, Problem 28.71P

(a)

To determine

The current passing through the entire cross section of the wire.

(b)

To determine

The magnetic field in the region r≥a.

(c)

To determine

The current contained in the cross section of the wire for r≥a.

(d)

To determine

The magnetic field in the region r≤a.

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Chapter 28, Problem 28.70P

Chapter 28, Problem 28.72P

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