Figure shows a cross section of a long conducting coaxial cable and gives its ra

Question

Figure shows a cross section of a long conducting coaxial cable and gives its radii (a, b, c). Equal but opposite currents i are uniformly distibuted in the two conductors. Derive expressions for B(r) with radial distance r in the range (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 =2cm, b=1.8cm, c=0.4 cm, and i=120A and plot the function B(r) over the range 0<r<3cm.

Figure shows a cross section of a long conducting coaxial cable and gives its radii (a, b, c). Equal but opposite currents i are uniformly distibuted in the two conductors. Derive expressions for B(r) with radial distance r in the range (a) r

Explanation / Answer

magnetic filed lines must be concentric cirlce both inside and outdie the wire.

for a closed radius ro

apply

closed int B.ds = B * 2piR -----------1

from Ampere RH rule, this is equal to Current times uo

so

at a point R, due to symmetric distributions

weget   I * pi R^2 = Io * Pi ro^2

so

I = r0^2/R^2 * Io

so

Amperes law becomes

B * 2pi R = uoI    = uo Io ro^2/R^2

so B = uoIoro/(2pi R^2)

now

part A: for r <c

B = uoio r/2pi c^2

-------------------

part B : C < r < b

we have

B = uoiob/2pi c^2

------------------------
part C:

B = uoiob^2/2pi a^2

-------------------

part D:

B = uoio/(2pi r)

--------------------------------

f.

B = 4*3.14 e-7 *120* 0.03^2/(2*3.14 * 0.004*0.004)

B = 48 mT

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