In a coaxial cable under TEM operation, which statement correctly describes the orientations of the electric (E) and magnetic (H) field lines? (Assume an ideal, uniform coax with inner conductor, dielectric, and outer conductor.)

Introduction:
Coaxial cables support a transverse electromagnetic (TEM) mode in which the electric and magnetic fields are entirely transverse to the direction of propagation. Recognizing the geometry of E and H field lines in a coax is essential for understanding impedance, shielding, and power flow.

Given Data / Assumptions:

• Ideal, uniform coaxial line with inner and outer conductors and homogeneous dielectric.
• Steady-state sinusoidal TEM propagation along the cable axis.
• No higher-order modes excited (below cutoff for non-TEM modes).

Concept / Approach:

In a coax, the electric field originates on the inner conductor and terminates on the inner surface of the outer conductor. Therefore, E lines are radial (pointing from inner to outer conductor). The magnetic field encircles the current flowing along the center conductor (and returns on the outer conductor’s inner surface), so H lines form concentric circles around the axis consistent with the right-hand rule. Power flows axially, with the Poynting vector S = E × H directed along the cable.

Step-by-Step Solution:

Verification / Alternative check:

Compute line impedance Z0 ≈ (60 / sqrt(εr)) * ln(b/a) for coax of inner radius a and outer radius b, derived from radial E and circular H distributions.

Why Other Options Are Wrong:

• Option b: swaps the roles of E and H.
• Option c: contradicts TEM field structure in coax.
• Option d: current direction flips H circulation but not field geometry (still circular), and E remains radial.
• Option e: E is not circular in coax; it is radial.

Common Pitfalls:

Confusing the right-hand rule’s sense of H with its geometry; direction reverses with current but the circular shape remains.

Final Answer:

The radial lines are E lines and the circular lines are H lines