Problem 28.56 Part A A coaxial cable carries a current Iwire in its inner conduc

Question

Problem 28.56 Part A A coaxial cable carries a current Iwire in its inner conducting wire and a current Ishell in its outer conducting shell. The radius of the wire is Rwire the distance from the cable center to the inside of the shell is Rshell, and the distance from the center to the outer edge of the shell is 2Rshell Determine all locations (if any exists) at which the magnetic field magnitude is zero if Iwire - Ishell Check all that apply O The magnetic field is zero in the region inside the shell, at a radius r Rshell The magnetic field is zero at the very center of the wire O The magnetic field is zero throughout all of the region outside the shell The magnetic field is zero in the region inside the shell, at a radius r = Rshell There is no location where the magnetic field is zero Submit My Answers Give Up Incorrect; Try Again; 3 attempts remaining

Explanation / Answer

Part A : Magnetic field = B
from ampere's law
consider imaginary circle of radius r
B*2pir = mu*I enclosed
so I enclosed = 0 at centre of wire
B = 0 at centre of wire
Part C : I wire = -I shell/2
from ampere's law
B*2pir = mu*I enclosed
now I enclosed has to be zero
this point has to be outside the wire
and I enclosed = I wire + I shell ( within the radius r)
I enclosed wire = I wire
I enclosed shell = I shell * pi(r^2 - (R shell)^2/pi((2R shell)^2 - (R shell)^2) = I shell*(r^2 - (R shell)^2)/(3(R shell)^2)
I shell*(r^2 - (R shell)^2)/(3(R shell)^2) = -I wire
I shell*(r^2 - (R shell)^2)/(3(R shell)^2) = I shell /2
2r^2 = (5(R shell)^2)
r = Rshell * sqroot(5/2)

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