Poynting's theorem in a solenoid

[matnatale]

Homework Statement

Consider a cylindrical solenoid(of radius a,and length h>>a,having n turns of wire for unity of lenght),The solenoid is connected to a resistance R and,at instant t=0 a current i(0)=i0 is flowing in the wire.Prove that poynting's theorem is verified for t>0[/B]

Homework Equations

[PLAIN]https://wikimedia.org/api/rest_v1/media/math/render/svg/e6fe1dabe8c9699364d0e983f92139c7a6d4deeb[/B]

The Attempt at a Solution

I assumed the current i(t) could be obtained solving Ldi/dt=Ri,where L is the inductance I previously computed.I tried to verify the conservation of energy applying the theorem in its global form on the volume of the solenoid,but,on one side,i don't know how to express current density J for the solenoid,on the other i realized it would lead me to a massive amount of calculations,Maybe there's some other way I didn't take into account?Sorry for my English.[/B]

 

[Baluncore]

Welcome to PF.
Maybe this will help.
https://en.wikipedia.org/wiki/Inductance#Inductance_and_magnetic_field_energy