In certain experimental fusion reactors, a magnetically confined plasma column acts as a variable dielectric medium for electromagnetic waves. Consider a cylindrical plasma column of radius R=5.0cm and length L=20cm. The plasma has a spatially varying dielectric constant given by ϵ(r)=ϵ0(1+αr2), where r is the radial distance from the axis and α=4.0×106m−2.
A thin cylindrical electrode of radius a=1.0cm is placed along the axis of the plasma column, and a grounded cylindrical electrode of radius b=3.0cm is placed concentrically around it. Both electrodes extend the full length of the plasma column.
(a) Find the capacitance per unit length of this coaxial configuration in the plasma medium.
(b) If a voltage V0=10kV is applied to the inner electrode, what is the total electrostatic energy stored in the system?
Given: ϵ0=8.85×10−12F/m