Electromagnetic field

Electromagnetic field
1. Consider a wave travelling in free space of frequency 1MHZ with electric field component is given by the expression E ?_((z,t) )= ?20?^3 sin(?t-ßz) a ^_z N/C. For this wave calculate
Propagation constant
Attenuation factor
c) Phase shift constant
2. An E.M. wave propagating in a free space has a phase shift constant ß=0.312 rad/m. The same wave has a phase shift constant of 1.51 rad/m upon entering a perfect dielectric. Assuming that µr = 1, determine:
The relative permittivity, er
b) The velocity of propagation, v of the wave in the dielectric.
3. For the given specifications given below, At a frequency of f = 9 MHz
a . Verify that copper (s=6.5×?10?^7 S/m,?_r=1 ) is a good conductor
b. quartz (s=?10?^(-15) S/m,?_r=4 ) is a good dielectric
4. a. Two solenoids are connected in series aiding manner such that linkage between them is 30%. If at a particular instance, the current in them is 3mA, calculate their magnetic energy. Both of them have 1.5mH and 1.8mH inductances respectively.
b. A solenoid has length l= 3m, N= 1500 turns, cross sectional radius r= 10cm, carries a current of I= 8A, and is kept in a medium with relative permeability of µ_r= 5.6. Calculate the energy stored in the solenoid.