The figure below is a cross-sectional view of a coaxial cable. The center conduc

Question

The figure below is a cross-sectional view of a coaxial cable. The center conductor is surrounded by a rubber layer, an outer conductor, and another rubber layer. In a particular application, the current in the inner conductor is = 1.10 A out of the page and the current in the outer conductor is I_2 = 2.96 A into the page. Assuming the distance d = 1.00 mm, answer the following. Determine the magnitude and direction of the magnetic field at point a. Determine the magnitude and direction of the magnetic field at point b.

Explanation / Answer

For some reason, I could not load the diagram. But since the question was well stated, I would guess that point a is in-between current I1 and I2. And point b is outside of I1 and I2. And as following Mr.Sturm's answer, I would guess the current I1 is outward meanwhile I2 is inward on the coaxial cable.


At point a, the distance is r = 0.001 m:

B = µI1 / 2r = ((4 x 10^-7 Tm/A) x 1.10 A) / (2 x 0.001 m)

B = 2.2 x 10^-4 T; Direction is upwards (towards the top).



At point b, the distance is R = 0.003 m :

. Effect by current I1 onto point b:

B1 = µI1 / 2R = ((4 x 10^-7 Tm/A) x 1.10 A) / (2 x 0.003 m)

B1 = 0.733 x 10^-4 T; Direction is upwards (towards the top)

. Effect by current I2 onto point b:

B2 = µI2 / 2R = ((4 x 10^-7 Tm/A) x 2.96 A) / (2 x 0.003 m)

= 1.973 x 10^-4 T; Direction is downwards (towards the bottom).

B = B2 - B1 = 1.24 x 10^-4 T = 124 uT

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