(a) show that the skin depth in a poor conductor (σ< < ωϵ) is (2/σ)ϵ/μ−−−√ (independent of frequency). find the skin depth (in meters) for (pure) water. (use the static values of ϵ, μ, and σ; your answers will be valid, then, only at relatively low frequencies.)
(b) show that the skin depth in a good conductor (σ> > ωϵ) is λ/2π (where λ is the wavelenght in the conductor.) find the skin depth (in nanometers) for a typical metal (σ≈107(ω m)−1) in the visible range (ω≈1015 /s), assuming ϵ≈ϵ0 and μ≈μ0. why are metals opaque?
(c) show that in a good conductor the magnetic field lags the electric field by 45∘, and find the ratio of their amplitudes. for a numerical example, use the "typical metal" in part (b).

a solenoid is created by wrapping a l = 90 m long wire around a hollow tube of diameter d = 4.5 cm.   the wire diameter is d = 0.9 mm.   the solenoid wire is then connected to a power supply so that a current of i = 9 a flows through the wire.

randomized variablesl = 90 m

d = 4.5 cm

d = 0.9 mm

i = 9 a                                          

write an expression for the number of turns, n, in the solenoid. you do not need to take into account the diameter of the wire in this calculation.

calculate the number of turns, n, in the solenoid.

write an expression for the length of the solenoid (l2) in terms of the diameter of the hollow tube d.

calculate the length of the solenoid (l2)   in meters.

calculate the magnitude of the magnetic field at the center of the solenoid in teslas.

explanation:

thermal energy is the answer