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## Main Question or Discussion Point

To calculate the displacement current in a coaxial cable (with equal and opposite currents on the inner and outer conductors), most standard texts use the magnetoquasistatic approximation, which ignores the time-varying electric field term in Ampere’s Law.

Using this approximation, the time-varying magnetic field is calculated by drawing a circular Amperian loop concentric with the inner cylinder (perpendicular to the axis of the cable). The magnetic field is phi-directed and azimuthally symmetric.

The induced electric field is then calculated by applying Faraday’s law to a rectangular loop with two sides parallel to the axis of the cable and the remaining two perpendicular. Of the two parallel sides, one lies in the region between the two conductors, and one outside. (This is the same geometrical arrangement that is used to calculate the magnetostatic field of a solenoid carrying a steady current). This gives a longitudinal electric field (ie parallel to the axis of the cable).

In the light of this, I have the following questions:

1. Does it make sense to calculate the induced electric field from the result obtained by ignoring it in the first place?

2. If the induced electric field is in the longitudinal direction, how does a coaxial cable support the TEM mode?

Using this approximation, the time-varying magnetic field is calculated by drawing a circular Amperian loop concentric with the inner cylinder (perpendicular to the axis of the cable). The magnetic field is phi-directed and azimuthally symmetric.

The induced electric field is then calculated by applying Faraday’s law to a rectangular loop with two sides parallel to the axis of the cable and the remaining two perpendicular. Of the two parallel sides, one lies in the region between the two conductors, and one outside. (This is the same geometrical arrangement that is used to calculate the magnetostatic field of a solenoid carrying a steady current). This gives a longitudinal electric field (ie parallel to the axis of the cable).

In the light of this, I have the following questions:

1. Does it make sense to calculate the induced electric field from the result obtained by ignoring it in the first place?

2. If the induced electric field is in the longitudinal direction, how does a coaxial cable support the TEM mode?