A solid cylindrical conductor is supported by insulating disks on the axis of a

Question

A solid cylindrical conductor is supported by insulating disks on the axis of a conducting tube with outer radius Ra = 6.85cm and inner radius Rb = 3.05cm . (Figure 1) The central conductor and the conducting tube carry equal currents of I = 3.65A in opposite directions. The currents are distributed uniformly over the cross sections of each conductor. What is the value of the magnetic field at a distance r = 4.43cm from the axis of the conducting tube?

What is the value of the magnetic field at a distance r = 4.43cm from the axis of the conducting tube? Recall that ?0=4?

A solid cylindrical conductor is supported by insulating disks on the axis of a conducting tube with outer radius Ra = 6.85cm and inner radius Rb = 3.05cm . (Figure 1) The central conductor and the conducting tube carry equal currents of I = 3.65A in opposite directions. The currents are distributed uniformly over the cross sections of each conductor. What is the value of the magnetic field at a distance r = 4.43cm from the axis of the conducting tube? no title provided What is the value of the magnetic field at a distance r = 4.43cm from the axis of the conducting tube? Recall that ?0=4???10?7 T?m/A.

Explanation / Answer

let I1 = 3.65 A

I2 = 3.65 A

at r = 4.43 cm

I_enclosed = I1 - I2*pi*(R2^2 - r^2)/(pi*(R2^2-R1^2)

= 3.65 - 3.65*(0.0685^2 - 0.0443^2/(0.0685^2-0.0305^2)

= 1 A

integral B.dl = mue*I_enclosed

B*2*pi*r = mue*I_elcosed

B = mue*I_enclosed/(2*pi*r)

= 4*pi*10^-7*1/(2*pi*0.0443)

= 4.5*10^-6 T <<<<<<----------Answer

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