Question

Interactive example does not help as much as you would think. Correct answer gets points!

Coaxial Cylindrical Conductors Two very long coaxial cylindrical conductors are shown in cross-section above. The inner cylinder has radius a = 2 cm and carries a total current of I1 = 1.4 A in the positive z-direction (pointing out of the screen). The outer cylinder has an inner radius b = 4 cm, outer radius c = 6 cm and carries a current of I2 = 2.5 A in the negative z-direction (pointing into the screen). You may assume that the current is uniformly distributed over the cross-sectional area of the conductors. What is Bx, the x-component of the magnetic field at point P which is located at a distance r = 5 cm from the origin and makes an angle of 30 degree with the x-axis? Bx = _____________ T

Answer 1

Applying Amperes law

B.dl=$\mu$₀I₁

B.a= $\mu$₀I₁

B1=$\mu$₀I₁/ (5-a)=(4$\times$3.14$\times$10^-7$\times$1.4) / 3= 5.8$\times$10^-7 T

The B1x= B1cos$\theta$ = 5.8$\times$10^-7(cos30)=8.9$\times$10^-8 T................1

Now    B₂= $\mu$₀I₂/ ( 5-b)= 4$\times$3.14$\times$10^-7$\times$2.5/( 5-4) =0.000003T

          B2x= Bcos (360-30)= 3$\times$10^-6 (0.86)=0.0000025T.............2

   B3= $\mu$₀I₂/ (c-5)= 4$\times$3.14$\times$10^-7$\times$2.5 / (6-5)= 0.00000314T

       B3x=B3cos(360-30) = 0.0000027T.......................3

Adding equ1 , eq2 and equ3

      B=B1x+B₂x + B₃x

         =(8.9$\times$10^-8) + (0.0000025) +0.0000027

       B =0.0000053T

This is the total magnetic field at point P