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

2024
Views:

157

Pages:

5
Author:

Jabin F.

Definition of magnetic dipole moment: For a current loop, M = I * A, where I is the current and A is the area of the loop. The direction of M is determined by the right-hand rule: Curl your fingers in the direction of the current, and your thumb will point in the direction of M. Magnetic dipole moment of a circular current loop: M = I * π * a^2, where a is the radius of the loop. Consideration of a loop as a point magnetic dipole: Similar to an electric dipole Example: Electron's orbital motion Given: Electron's charge (e), velocity (vo), and Bohr radius (a₀) Current: I = e / T = ev₀ / (2πa₀) Magnetic dipole moment: M = (ev₀a₀ / 2) * (-ẑ) Gyromagnetic ratio: γ = e / (2m) Top Section A circuit diagram with a resistor, a capacitor, and a voltage source. Equations: V(t) = V₀ * cos(ωt) i(t) = (V₀ / R) * sin(ωt) E = (1/2) * CV₀² Bottom Section A diagram of a capacitor with electric field lines and charge distribution. Equations: E = (1/2) * ε₀ * E₀² Jd = (1/4π) * ε₀ * dE / dt Jd = -(1/4π) * ε₀ * V₀ * ω * sin(ωt) E = -(1/2) * ε₀ * E₀² * sin²(ωt) Jd = (1/2) * ε₀ * E₀² * sin(2ωt) S = (1/4π) * ε₀ * E₀² Given: Equation: E = (2k̂ - 3ĵ) * 10⁻³ * sin[10⁷(x + 2y + 3z - βt)] Calculations: R = √(1² + 2² + 3²) = 10√14 |k̂| = 10 * √(1 + 4 + 9) = 10√14 ω = 10⁷β ω = c / R β = c / (10⁷ * √14) = √14 * c Conclusion: β = √14 * c (Option - a)