A plane wave E =10 sin (ωt-10x) ay V/m in lossless medium (ε=ε0, µ=5µ0) encounters a lossy medium (ε=4ε0, µ=µ0,σ=0.1 S/m) normal to the x-axis at x=0. Examine i) Reflection coefficient (Γ) and VSWR(S) Total electric and magnetic field intensity(E,H)

The reflection coefficient (Γ) and the Voltage Standing Wave Ratio (VSWR) can be calculated using the formulas for the reflection of electromagnetic waves at a boundary between two media.

i) Reflection coefficient (Γ) and VSWR(S)

The reflection coefficient (Γ) is given by:

Γ = (Z2 - Z1) / (Z2 + Z1)

where Z1 and Z2 are the impedances of the two media. The impedance of a medium is given by:

Z = sqrt(µ/ε)

For the lossless medium, we have ε = ε0 and µ = 5µ0, so:

Z1 = sqrt(5µ0/ε0)

For the lossy medium, we have ε = 4ε0, µ = µ0, and σ = 0.1 S/m. The impedance of a lossy medium is given by:

Z2 = sqrt(µ/ε + jωσ)

Substituting these values into the formula for Γ, we can calculate the reflection coefficient.

The Voltage Standing Wave Ratio (VSWR) is given by:

S = (1 + |Γ|) / (1 - |Γ|)

Substituting the value of Γ calculated above, we can find the VSWR.

ii) Total electric and magnetic field intensity(E,H)

The total electric field intensity (E) is given by the sum of the incident and reflected fields:

E = Ei + Er

where Ei is the incident field and Er is the reflected field. The incident field is given by the plane wave:

Ei = 10 sin (ωt - 10x) ay V/m

The reflected field is given by:

Er = ΓEi

Substituting the value of Γ calculated above, we can find the total electric field intensity.

The total magnetic field intensity (H) is given by the sum of the incident and reflected fields:

H = Hi + Hr

where Hi is the incident field and Hr is the reflected field. The incident field is given by:

Hi = Ei / Z1

The reflected field is given by:

Hr = Er / Z2

Substituting the values of Ei, Er, Z1, and Z2 calculated above, we can find the total magnetic field intensity.