Question

Is the field inside the inner conductor 0 ? Why?

Why is the field outside the outter conductor 0?

Please answer

4.32 A long coaxial cable has an inner conductor with radius a and outer conductor with radius b. If the inner conductor has p, p, where po is a constant, determine E everywhere.

Answer 1

The modified diagram is, Gaussian cylinders 'ام - 2. Z-axis 1. For the region p<a, consider gaussian cylinder 1, with radius p and length L along Z-axis. From Gauss law, $ Ē. d5 = Lenclosed S EO Lenclosed by Gaussian cylinder 1 = 0 Hence, E=0

For the region a<p<b, consider gaussian cylinder 2, with radius pand length L along z-axis. From Gauss law, . d5 = Perekond Lehed = Lg Ps as Ps= PC'm Hence, Cerita = @ Jadøds Darbo = ([=– 48 (271) $Ē.dS = I J E ā.pdødzā, = E,()[1" [=] 2 L $=0 ==0 = E. (27L) From Gauss law, E, (21L) p=“20 (21L)

= Popā, V/m Ep For the region p>b, consider gaussian cylinder 3, with radius p and length L along Z-axis. From Gauss law, Qerciced = apo (27L) Since, charge enclosed by Gaussian cylinder 3 is same as charge enclosed by Gaussian cylinder 2. Hence, I Ep? = apozā, V/m EP

In general, coaxial cable inner conductor and outer conductor have equal magnitude of charges and opposite in sign. Here, surface charge density on inner conductor is given but not given for outer conductor. If outer conductor carries same magnitude of charge as inner conductor with negative sign, then for region p>b, electric field will be zero.