University:
Santa Fe College
Course:
ETS 2527C | Electromechanical Components and Mechanisms
Academic year:

2024
Views:

472

Pages:

6
Author:

Jabin F.

Title: Comparison between Mechanical and Electromagnetic Systems Main Points: Current-carrying coils store magnetic energy: The energy stored in a coil is given by U_m = (1/2) * L * I². Charged capacitors store electric energy: The energy stored in a capacitor is given by U_e = (1/2) * C * V². Electromagnetic energy: The total electromagnetic energy is the sum of the magnetic and electric energies: U_em = (1/2) * L * I² + (1/2) * C * V². Total energy of a mechanical system: The total energy of a mechanical system is given by E_total = (1/2) * m * v² + (1/2) * k * x². Comparison of Mechanical and Electromagnetic Systems: Both systems have kinetic and potential energy components. In electromagnetic systems, the potential energy is stored in electric and magnetic fields. The equations for energy in the two systems have similar forms. Question 22: Given: Ē = E₀(3î + 4ĵ) cos(kx - ωt) Free space (isotropic and non-dispersive medium) Find: Direction of 𝐵 Direction of 𝑆 Solution: Direction of 𝐵: 𝐵 = (1/ω) * (𝑘 × Ē) 𝑘 = 4𝑘₂î - 3𝑘₃ĵ 𝑘 × Ē = 16𝑘₂𝑘₃î + 9𝑘₂𝑘₃ĵ 𝐵 = (16𝑘₂𝑘₃î + 9𝑘₂𝑘₃ĵ) / ω Direction of 𝐵 is proportional to (4𝑘₂ - 3𝑘₃)î + (3𝑘₂ + 4𝑘₃)ĵ Direction of 𝑆: 𝑆 = Ē × 𝐵 𝑆 = (3î + 4ĵ) × (16𝑘₂𝑘₃î + 9𝑘₂𝑘₃ĵ) / ω 𝑆 = 40𝑘₂𝑘₃î - 33𝑘₂𝑘₃ĵ Direction of 𝑆 is proportional to 4î - 3ĵ Question 21: Polarized in the y-direction Mean E.F. in y-direction Question 19: Amplitude of E_f = E₀ Intensity (I) = (1/2) * ε₀ * E₀² Calculations: E₀ = √(2I / (ε₀ * c)) E₀ = √(2 * 10 * 150 / (3 * 10^8 * 8.85 * 10^-12)) E₀ = 10.62 V/m Question 18: ⟨u_em⟩ = (1/4) * ε₀ * E₀² Conclusion: The correct option for question 18 is (a). Question 16: 𝐵 = B₀ sin(kz - ωt) * 𝑘̂ Free space (by default) Solution: 𝑅 = -(𝑘 / (2ω)) * (𝑐² + 1) * 𝑘̂ Ē = (𝑘 × 𝐵) / μ₀ = (𝑘 × (B₀ sin(kz - ωt) * 𝑘̂)) / μ₀ Ē = (c² / μ₀) * B₀ * [(-j) * sin(kz - ωt)] * 𝑘̂ Question 17: 𝑆 = (Ē × 𝐵) / μ₀ ⟨S⟩ = (c / μ₀) * B₀² * (1/2) Direction of 𝑅 is the same as the direction of ⟨S⟩ Conclusion: The correct option for question 17 is (a).