Question 54: Magnetism and Matter

Question

In a co-axial straight cable, the central conductor and the outer conductor carry equal currents in opposite directions. The magnetic field is zero :

Accepted Answer

Let's dig into how the magnetic field behaves in a coaxial cable in relation to the given options. The principle to consider here is AmpÃÂ¨re's law, which states that the magnetic field in a loop surrounding a current is proportional to the amount of current enclosed. When we apply this to a coaxial cable, we must look at different regions within the cable.
Option A: Inside the outer conductor
The magnetic field within the outer conductor is not zero because the current in the outer conductor itself contributes to the magnetic field in that region. However, considering the symmetric distribution of current and the geometry of the coaxial cable, there may be a varying magnetic field within the conductor depending on the distance from the center axis.
Option B: Outside the cable
Outside the coaxial cable, the net current enclosed by a path enclosing both conductors is zero because the current in the inner conductor flows in the opposite direction to the equally magnitude current in the outer conductor. These currents being equal and opposite in direction cancel each other out, leading to a net enclosed current of zero. According to AmpÃÂ¨re's law, if the net enclosed current is zero, the magnetic field in that space is also zero. Therefore, the magnetic field is zero outside the cable.
Option C: In between the two conductors
In the space between the two conductors, the magnetic field is not zero. This region only encloses the current from the inner conductor. The magnetic field in this region is due to the current in the inner conductor and follows the right-hand rule, which would result in concentric circles of magnetic field around the inner conductor. Since only the inner conductor's current contributes to the magnetic field in this space, AmpÃÂ¨re's law suggests that there is a non-zero magnetic field in this region.
Option D: Inside the inner conductor
Within the inner conductor, the magnetic field is not necessarily zero. Like within the outer conductor, the magnetic field inside the inner conductor will depend on the distribution of the current within that conductor. Utilizing the formula derived from AmpÃÂ¨re's law for a cylindrical conductor with a uniform current distribution, the magnetic field inside the conductor increases linearly with the distance from the center axis up to the conductor's surface.
In conclusion, the correct option, based on AmpÃÂ¨re's law and the principle that the net current enclosed determines the magnetic field outside the current's path, is:
Option B: Outside the cable
This is because the equal and opposite currents in the inner and outer conductors cancel each other, leading to a net magnetic field of zero outside the coaxial cable.

Answer

inside the outer conductor

Answer

outside the cable

Answer

in between the two conductors

Answer

inside the inner conductor

Magnetism and Matter

In a co-axial straight cable, the central conductor and the outer conductor carry equal currents in opposite directions. The magnetic field is zero :

Choose the correct answer: