A coaxial cable carries a current I wire in its inner conducting wire and a curr

Question

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 isRshell, 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.

There is no location where the magnetic field is zero.

part c

Determine all locations (if any exists) at which the magnetic field magnitude is zero if Iwire = Ishell/2.

Check all that apply.

The magnetic field is zero at the very center of the wire. 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=Rshell12 The magnetic field is zero in the region inside the shell, at a radius r=Rshell52

There is no location where the magnetic field is zero.

part c

Determine all locations (if any exists) at which the magnetic field magnitude is zero if Iwire = Ishell/2.

Check all that apply.

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=Rshell52 The magnetic field is zero at the very center of the wire. The magnetic field is zero in the region inside the shell, at a radius r=Rshell12 There is no location where the magnetic field is zero.

Explanation / Answer

1) The magnetic field is zero at the very center of the wire.

2) The magnetic field is zero at the very center of the wire.

The magnetic field is zero in the region inside the shell, at a radius r=Rshell*sqrt(5/2)

Ishell*(r^2 - R^2)/((2*R)^2 - R^2) = Iwire

2*Iwire*(r^2 - R^2)/((2*R)^2 - R^2) = Iwire

2*(r^2 - R^2) - 3*R^2

r^2 - R^2 = (3/2)*R^2

r^2 = R^2 + (3/2)*R^2

r = sqrt(5/2)*Rshell

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