Question 12/00
COAXIAL CABLE
A coaxial cable is built of two parallel metal cylinders of
arbitrary cross-section. If current is flowing in the inner cylinder
and an equal and opposite current is flowing in the outer cylinder,
then magnetic field will be present inside the cable, and one can define
inductance L per unit length of the cable. Similarly, one can charge
the inner and outer cylinders with opposite charges, and view it as a capacitor
with capacitance C per unit length of the cable. Show that expression
(LC)1/2 is independent of the shape of the cross-sections and find
its value.
This was a homework question in the course of Applied Electromagnetism given
by Y. Kantor in 1996-99.
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