Electromagnetic theory miscellaneous
- Consider two fields
E = 120 π cos (106 πt – βx) ay V/m
and H = A cos (106 πt – βx) az A/m
The values of A and β which will satisfy the Maxwell's equation in a linear isotropic homogeneous lossless medium with εr = 8 and µr = 2 will be—A (in A/m) β (in rad/m) A. 1 0.0105 B. 1 0.042 C. 2 0.0105 D. 2 0.042
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We know that
η = √ μ = √ μrμ0 ε εrε0 we get →H = → E ⇒ → E η 120 π
→H = cos (106πt − β X)az
→H = A cos (106πt − β X)A = 120 π η = 120 π √ μrμ0 εrε0 = 120 √ μr (120π) ε0 A = √ εr μr = √ 8 = 2 2 for the lossless homogeneous medium phase velocity = ω β
given, ω = 106 πv = 106π and v = c β √μrεr = 3 × 108 √16 ∴ β = 4 × 106 × π ⇒ 4 × π = 0.042 3 × 108 300 Correct Option: D
We know that
η = √ μ = √ μrμ0 ε εrε0 we get →H = → E ⇒ → E η 120 π
→H = cos (106πt − β X)az
→H = A cos (106πt − β X)A = 120 π η = 120 π √ μrμ0 εrε0 = 120 √ μr (120π) ε0 A = √ εr μr = √ 8 = 2 2 for the lossless homogeneous medium phase velocity = ω β
given, ω = 106 πv = 106π and v = c β √μrεr = 3 × 108 √16 ∴ β = 4 × 106 × π ⇒ 4 × π = 0.042 3 × 108 300
