Question

Two types of dielectric material are inserted between cylindrical conductors with radius a, length L, and radius c, length L (Figure 6). 
Calculate the following when the dielectric rate of a section (a<ρ≤b) is εb, and the dielectric rate of section (b<ρ<c) is εc.

a)When an internal conductor has a charge of Q, an external conductor has a charge of -Q, calculate the inside surface charge density of ρa and the outer surface charge density of ρc respectively.

b)Find Electric Field E in Zone (a<ρ≤b) and (b<ρ<c) respectively.

c)Find the potential difference between the two conductors

d)Use the above results to obtain Capacitance.

Answer 1

Given length L of two conductors of inner radius a and outer radius C. let the space between the conductors be filled with a dielectric with permittivity e. The conductors 1 and 2, respectively carry + Q and -Q uniformly distributed on them. Internal conductor have + Q external conductor have -Q \r\n Inside charge density P_a we know Q = integral D^vector: dS^vector Q = e contourintegral E^vector . dS^vector Q = P_s ds Q = P_a ds P_a = Q/S = Q/2 pi PL a = radius of internal conductor P_a = Q/2 pi aL L rightarrow length of the conductor \r\n outer surface charge density Q = P_S^vector dS^vector P_S = P_C Q = P_C . dS -Q Surface area = P_C P_C = -Q/2 pi p L here radius of external conductor = C then P_C = -Q/2 pi C L \r\n L rightarrow length of the conductor p_C = -Q/2 pi C L