A thick-walled copper pipe (inner radius and outer radius b) is centered on the
ID: 2191730 • Letter: A
Question
A thick-walled copper pipe (inner radius and outer radius b) is centered on the z-axis and carries a current density of magnitude J(r)=Br . (The parameter B has units A/m^3.) A wire runs parallel to the pipe a distance R= 2b away from the z-axis.
(a) What is B=|B ? |, the magnetic field magnitude, inside the pipe (r<a), inside the copper itself (a<r<b), and outside the pipe (r>b )?
(b) Sketch a plot of the field magnitude B(r). Be sure to clearly label the axes of your plot, the value of the maximum Bmax, the inner and outer radii a and b, and how B(r) depends on r in each region described in part (a).
(c) Suppose that a current Iw flows in the wire at R=2b. What force does the wire exert on the pipe if Iw flows in the same direction as Ip, the total current in the pipe?
Explanation / Answer
(a) Using Gauss' Law, the magnetic field inside the conductor is 0 (an amperian loop encloses no current). (b) For aRelated Questions
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