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Two very long coaxial conductors.. Two very long coaxial cylindrical conductors

ID: 1309537 • Letter: T

Question

Two very long coaxial conductors..

Two very long coaxial cylindrical conductors are shown in cross-section above. The inner cylinder has radius a = 5.00 cm and carries a total current of I1 =1.40 A in the positive z-direction (pointing out of the screen). The outer cylinder has an inner radius b = 10.0 cm, outer radius c = 15.0 cm and carries a current of I2 = 2 20 A in the negative z-direction (pointing into the screen). You may assume that the current is uniformly distributed over the cross-sectional area ot the conductors. What are the magnitude and direction of the magnetic field at point P at r = 12 0 cm?

Explanation / Answer

Ampere Circuital law

integral(B.dl) = mu0*I_inside

Taking a circular contour of radius r(= 0.12 m) and applying this law

B*2*pi*r = mu0*I_inside

I_inside = 1.40-2.20*(pi*(r^2-b^2)/(pi*(c^2-b^2)) in + z direction

   = 1.40 - 2.2 * (0.12^2-0.1^2)/(0.15^2-0.12^2) = 0.205 A

B = 4*pi*10^-7* 0.205 / (2*pi*0.12) = 3.42*10^-7 T

By right hand law, since current is outward, B is counter clockwise and tangential at point P.