11.37 Time-Harmonic Fields. The electric field intensity
E ¼ ^x10πcos 106t 50z
þ ^y10πcos 106t 50z
½V=m
is given in a linear, isotropic, homogeneous medium of permeability μ0 [H/m] and permittivity ε0 [F/m]. Write the
magnetic field intensity and the magnetic flux density:
(a) In terms of the time-dependent electric field intensity.
(b) In terms of the time-harmonic electric field intensity.
11.38 Time-Harmonic Fields. The magnetic field intensity in free space is given as H ¼ ^xHx þ ^yHy þ ^zHz
ejβzejϕ [A/m],
where Hx, Hy and Hz are complex numbers given as Hx ¼ hx + jgx, Hy ¼ hy + jgy and Hz ¼ hz + jgz:
(a) What is the time-dependent magnetic field intensity H in air?
(b) Write the magnetic field intensity in terms of amplitude and phase.
11.39 Two vector fields are given in phasor form as
E1 ¼ ^xð20 þ j20Þe j0:3πz þ ^yð10 j20Þe j0:3πz, E2 ¼ ^xð20 j10Þe j0:3πz þ ^yð20 þ j20Þe j0:3πz ½V=m
Calculate:
(a) The time domain representation of the two fields.
(b) The sum E1 + E2 in phasor form and in the time domain.
(c) The difference E1 – E2 in phasor form and in the time domain.
(d) The vector product of the two fields in the time domain and in phasor form.
(e) The scalar product of the two fields in the time domain and in phasor form.