Poynting Vector on the surface of current carrying conductor

A straight conducting wire of circular cross section, radius a, has a resistance R per unit length and carries a constant current I. Find the value and direction of the Poynting vector at the surface of the wire, and hence show that the total power entering the wire per unit length is (I^2)R. By considering the divergence of the poynting vector inside the wire, show that the energy is dissipated uniformly through it's volume.

An infinite wire having current I oriented along z-axis passes through a small hole in a uniformly charged infinite plane at z = 0. Thecurrent is perpendicular to the charged plane (with charge density σ) . Find thePoyntingvector in vacuum and explain the result.

Consider a spherical conductor of radius R. Inside of it are two spherical cavities A and B, with radii a and b, respectively. Each cavity contains a point charge qa and qb, respectively. Find thesurface charges for all three surfaces (R, the outer surfaces of theconductor, and thesurfaces of the inner cavities A and B) and t

An infinitely long solid cylindrical conductor of radius R carries a free current density J(s) = Cs^3z distributed over its cross section. The z axis is the long axis of the cylinder. Theconductor has a permeability 'mu' which does not equal 'mu-0'. Outside theconductor is a vacuum.
A. Find H, B, M inside theconductor and

Light is directed on thesurface of the non-conductive material at an angle of incidence of pi/6, just outside of this surfacethe intensity is 50(W/M^2). The EM wave is polarized in the plane of incidence.
1. Find the E0 and B0 outside the material.
2. Find the pointing vector outside the material.
3. What is the intens

See attached file for illustration.
The figure shows a hollow cavity within a neutral conductor. A point charge Q is inside the cavity.
What is the net electric flux through the closed surface that surrounds theconductor?

A set of problems on magnetic effects of current viz. magnetic field, force experienced by a conductor/charge moving in a magnetic field etc.
See attached file for full problem description.

If a wire is placed next to the face of a permanent magnet and a current sent through the wire, then a Lorentz force is present orthogonal to both the direction of thecurrent and the magnetic field. I would assume there should be a linear force on the magnet in the other direction, but the magnetic field caused by thecurrent i

Let S be the part of the plane which lies in the first octant, oriented upward. Find the flux of thevector field across thesurface S.
Please see the attached file for the fully formatted problems.