A length of coaxial line has a solid inner conductor of radius and a thin outer…
PHYSICS · Multi-part · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Conductors, capacitance and boundary-value electrostatics · Conductors, capacitance and boundary-value electrostatics
Electricity, Magnetism and Electromagnetism, Ch Conductors, screening and capacitance
Problem
A length l=2.0m of coaxial line has a solid inner conductor of radius a=1.0mm and a thin outer conducting sheath of inner radius b=4.0mm; the space between them is vacuum. Treat the cable as long enough for the field between the conductors to be radial, so that the capacitance of such a cable is C=2πε0l/ln(b/a), as derived in this chapter. A charge +0.50nC is placed on the inner conductor; the sheath carries no net charge and is isolated, and no other charges are nearby. Equilibrium has been reached.
((a)) State the total charge on the inner surface of the sheath and on its outer surface.
((b)) Find the capacitance of the cable and the potential difference between the two conductors.
((c)) Find the energy stored in the field between the conductors.
((d)) Two such identical cables are connected in parallel (inner to inner, sheath to sheath). Find the capacitance of the pair.