**Problem Statement**An infinitely long cylindrical tube, of radius \(a\), moves at constant speed \(v\) along its axis. It carries a net charge per unit length \(\lambda\), uniformly distributed over its surface. Surrounding it, at radius \(b\), is another cylinder, moving with the same velocity but carrying the opposite charge (\(-\lambda\)). Find:(a) The energy per unit length stored in the fields.(b) The momentum per unit length in the fields.(c) The energy per unit time transported by the fields across a plane perpendicular to the cylinders.

For each of the three regions, the electric field resulting from the infinitely long charged cylindrical shells with radii of a and b, respectively, can be expressed as follows:( assume axis as the z-axis )For s < aFor a < s < bFor s > bUsing Gauss's law, the electric field for the specific regions can be calculated.To calculate the expression for the electric fields in the various regions, take into consideration a Gaussian surface inside the inner cylindrical shell with radius s and height L. Then, use Gauss law.In a similar way, the expression for the magnetic field B in the regions s < a and s > b will be zero and in the region a < s < b, it will be expressed using Ampere’s law as,In this case, the cylindrical coordinate system has been used for the unit vectors because the problem involves cylindrical symmetry.The total energy stored in the electromagnetic fields per unit volume denoted by u is expressed as,Substitute equations (1) and (2) in the above equation and simplifyTherefore the energy per unit length W/l stored in the Electromagnetic fields is calculated as,b)The expression for the momentum density g is given by,Here S is the Poynting’s vector.The momentum per unit length p/l can be calculated from the above expression using equations (1) and (2) and further integrating as.c)The energy transported per unit area per unit time is calculated using the Poynting’s vector given by,Therefore the energy per unit time transported by the field across a plane perpendicular to the cylinders is given by