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CBSE Class 12-science Answered

A coaxial cable consists of inner conductor of radius 0.02 m and thin outer conductor of radius 0.06 m. What current is needed in this cable to produce a magnetic field of 10-5 T at a point located at a distance 0.03 m from the axis of the cable?
Asked by Topperlearning User | 08 May, 2015, 10:30: AM
answered-by-expert Expert Answer

To evaluate the magnetic field between the wires, we draw a circular path of radius r between the wires (R1 < r < R2) as in the figure.

 Now we have begin mathsize 11px style B with rightwards arrow on top times stack d l with rightwards arrow on top space equals space B d l space cos space theta space equals space B left parenthesis 2 πr right parenthesis space equals space straight mu subscript 0 straight I end style where I is the total current flowing through the area enclosed by the path.

              

 

Since r < R2, the only current flowing through this area is that in the inner conductor which is I. This once again gives that begin mathsize 11px style straight B space equals space fraction numerator straight mu subscript 0 straight I over denominator 2 πr end fraction end style

Since this point is located between the cylinders (0.02 < 0.03 < 0.06)

Thus B = begin mathsize 11px style fraction numerator 4 straight pi space cross times space 10 to the power of negative 7 end exponent space cross times space straight I over denominator 2 straight pi space cross times space 0.03 end fraction end style

Substituting for B = 10-5 T

We have I = 1.5 A.

Answered by | 08 May, 2015, 12:30: PM

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