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 11 1.16 A out of the page and the cumentin the outer conductors 3.1 Anto the page. Assuming the distance d 1.00 mm, answer the following. (t (a) Determine the magnitude and direction of the magnetic field at point a magnitude direction upward (b) Determine the magnitude and direction of the magnetic field at point b. 400 You can approach this problem by finding the field produced by current 11 and the field produced by 12 and then adding them vectorially· magnitude direction downward

Explanation / Answer

At point a

using

Ampere's law

B*dl = mu_o*I

mu_o is the permeability of free space

B*(2*pi*r1) = (4*3.142*10^-7*1.16) = 1.46*10^-6

B = 1.46*10^-6 /(2*3.142*1*10^-3)

B = 2.32*10^-4 T

B = 232*10^-6 T = 232 uT

direction is Upwards

b) at point b

using ampere's law

B*dl = (mu_o*I2)

B*2*pi*r2 = mu_o*I2

B = (4*3.142*10^-7(3.16-1.16))/(2*3.142*3*10^-3)

B = 1.33*10^-4 T

B = 133*10^-6 T

B = 133 uT

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