If a long hollow copper pipe carries a direct current, the...

If a long hollow copper pipe carries a direct current, the magnetic field associated with the current will be
(a) Only inside the pipe
(b) Only outside the pipe
(c) Neither inside nor outside the pipe
(d) Both inside and outside the pipe

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Key Concepts

Ampere’s Law

Ampere’s Law relates the magnetic field around a closed loop to the net current enclosed by that loop. In scenarios with high symmetry, such as a long cylindrical conductor, this law simplifies the determination of the magnetic field by showing that if no current is enclosed, the net magnetic field along the path is zero.

Magnetic Field Distribution in Current-Carrying Conductors

When a conductor carries a steady current, it produces a magnetic field that circulates around it. The spatial distribution of this field depends on how the current is distributed within the conductor. In the case of a hollow conductor, the magnetic field within the hollow region is zero because an Ampèrian loop in that region encloses no current, while there is a nonzero magnetic field outside the conductor where the full current is enclosed.

Symmetry in Electromagnetic Problems

Symmetry greatly simplifies electromagnetic analyses by reducing complex field patterns to more manageable forms. In cylindrical configurations like a long hollow pipe, symmetry ensures that the distribution of the magnetic field is uniform and predictable, leading to an absence of magnetic field in the hollow (current-free) region and a well-defined field outside where the net current is enclosed.

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