My question is under attachment. ### 2nd Question:For the same coaxial cable of the previous question, now carrying a uniformly distributed current \(I\), find the following. Assume permeability of free space in all regions.1. The magnetic field \(H\) for both \(r < a\) and \(a < r < b\).2. The "external" inductance per unit of length corresponding to the magnetic field in the region \(a < r < b\).3. The internal inductance per unit of length corresponding to the magnetic field inside the interior conductor. Comment on your result.**Hint:** Use the internal magnetic field found in (1) to calculate the magnetic energy density. Then integrate that to find the total energy inside the conductor per unit of length. Use the relationship between energy stored and inductance to find the value of the inductance. 1st Question:A coaxial cable consists of an internal solid cylindrical conductor of radius \(a\) and a cylindrical conductive shell of radius \(b\) separated by a dielectric of permittivity \(\varepsilon\). Assuming the length of the cable as infinite and that it carries an electric charge of \(q_1\) coulombs/meter, find the following:1. The electric field \(E\) for \(a < r < b\) *Note: \(r\) is the cylindrical radius.*2. The voltage difference between the two conductor surfaces.3. The voltage \(V(a)\), assuming \(V(b) = 0\).4. Since the maximum value of the electric field occurs at the surface \(r = a\), and that value cannot exceed the value \(E_{\text{max}}\) that causes the dielectric breakdown, find the relation between \(a\) and \(b\) that makes the potential difference between the conductors the maximum possible. *Hint: Use the expressions of \(E\) and \(V\) found in (1) to (3) to relate \(V(a)\) and \(E(a)\), therefore eliminating \(q_1\) from the equations. Then find the maximum of \(V(a)\) as a function of \(a\), with \(E(a) = E_{\text{max}}\) and \(b\) constant.*5. Assuming that the dielectric breakdown occurs for \(E_{\text{max}} = 10 \text{ kvolts/cm}\), and that \(a = 0.1 \text{cm}\), find the maximum voltage the cable can carry.

-Coaxial cables, commonly called coax, are copper cables with metal shielding designed to supply immunity against noise and greater bandwidth.-Coax can transmit signals over larger distances at the next speed as compared to twisted pair cables.-Coax features a central core of stiff copper conductor for transmitting signals. This is covered by an insulant. The insulator is encased by a closely woven braided metal outer conductor that acts as a shield against noise.The outer conductor is again enclosed by a plastic insulating cover. The longitudinal (axial) field profiles Ez(ρ) for the circular symmetric principal TM propagation mode in typical coax at frequencies of 1 MHz and 20 kHz. The ratio of the complex Ez(ρ) field value divided by the whole current I (integrated within the cross-section) at a hard and fast value of z. the present I in inner and outer conductors are, for any frequency, The familiar lateral directed fields Hφ(ρ) and Eρ(ρ) are much simpler in form and within the dielectric between the conductors have an almost exact 1/ρ lateral dependence. Plotting Ez(ρ)/I which is in units of Ω/m, is helpful because the values of this quantity at Ri (the radius of the inner solid conductor) and at Ro (the inner radius of the outer tubular conductor). the important and imaginary parts are simply the series resistances and (inductive) reactance of the corresponding conductors. When the external distributed inductive reactance is added to those, the result is Z.The longitudinal current density at any point within the conductors is simply the conductor conductivity times the Ez field at that time. Note that since the Ez field is complex, this suggests that there's a phase shift effect within the Ez field as a function of the radial distance ρ. The plots show the important and imaginary parts and also the magnitude of Ez(ρ). These plots represent the Ez component's field amplitude dependence on ρ for a wave propagating within the + z direction. the entire field dependence for this component of the sector, including the temporal and z (propagation direction) dependence is: