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Figure 29-88 shows a cross section of a long conducting

Chapter , Problem 87

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QUESTION:

Figure 29-88 shows a cross section of a long conducting coaxial cable and gives its radii (a, b, c). Equal but opposite currents i are uniformly distributed in the two conductors. Derive expressions for B(r) with radial distance r in the ranges (a) r + c,(b) c + r + b, (c) b + r + a, and (d) r , a. (e) Test these expressions for all the special cases that occur to you. (f) Assume that a ! 2.0 cm, b ! 1.8 cm, c ! 0.40 cm, and i ! 120 A and plot the function B(r) over the range 0 + r + 3 cm

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QUESTION:

Figure 29-88 shows a cross section of a long conducting coaxial cable and gives its radii (a, b, c). Equal but opposite currents i are uniformly distributed in the two conductors. Derive expressions for B(r) with radial distance r in the ranges (a) r + c,(b) c + r + b, (c) b + r + a, and (d) r , a. (e) Test these expressions for all the special cases that occur to you. (f) Assume that a ! 2.0 cm, b ! 1.8 cm, c ! 0.40 cm, and i ! 120 A and plot the function B(r) over the range 0 + r + 3 cm

ANSWER:

Problem 87

Figure 29-88 shows a cross section of a long conducting coaxial cable and gives its radii (a, b, c). Equal but opposite currents i are uniformly distributed in the two conductors. Derive expressions for B(r) with radial distance r in the ranges (a) r < c,(b) c < r < b, (c) b < r < a, and (d) r >a. (e) Test these expressions for all the special cases that occur to you. (f) Assume that a = 2.0 cm, b = 1.8 cm, c = 0.40 cm, and i = 120 A and plot the function B(r) over the range 0 + r + 3 cm

                                                        Step by Step Solution

Step 1 of 8

The Ampere’s Law can be expressed as,

Where,  is the permeability of the free space and ienc is the net current enclosed within the ampere’s loop.

The law is used when the magnetic field produced is symmetrical about the cross-section.

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