Coaxial Cable Capacitor: A coaxial cable of length L, as shown in the sketch below, is formed by two concentric, cylindrical perfect conductors

Coaxial Cable Capacitor: A coaxial cable of length L, as shown in the sketch below, is formed by two concentric, cylindrical perfect conductors. The inner conductor has a radius a; the inner radius and outer radius of the outer conductor shell are 15 and c, respectively. L >> 6, so ignore the ?inging ?eld e?ecr at the ends ofthe cable. The space between the conductors is ?lled by a perfect dielectric medium of £1. Determine the capacitance per unit length of this system, C ’, using the follow two methods: a. Laplace’s equation and boundary conditions by assuming that a voltage is applied to the inner conductor, V = Va and the outer shell is grounded. b. Gauss’s law by assuming a positive charge per unit length, 0', on the surface of the inner conductor. Show your work details for full credit. Cross~section of the cable