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

2024
Views:

216

Pages:

5
Author:

Jabin F.

Section 1: Electric Field at Displaced Conductor Electric field at displaced Cond'n E = 1/(4πε₀(a-r)²) + 1/(4πε₀(a-r)²) + ... (a long equation with multiple terms) E = q/(4πε₀)[(b+x)² - (a-x)²]/(a²-x²)²](+x) E = 2(4an)/(4πε₀(a²-x²)²)(+x) (equation labeled (i)) Section 2: Force on q' Force on q' F = 2q'(4an)/(4πε₀(a²-x²)²) F = 2q'(4ax)/(4πε₀(a⁴)) F = 2q'/(4πε₀a³) (equation labeled (3)) Section 1: Force and Oscillations S.H.M force F = Kn (equation labeled (1)) K = force constant / spring constant K = 2q'/(ππε₀a³) (equation labeled (5)) frequency of oscillation (S.H.M) ω = √(k/m) ω = √(2q'/(ππε₀a³m)) Time period T = 2π/ω = 2π√(m/k) T = 2π√(ππε₀a³m/(2q')) Section 2: Electric Field Now if we displaced on y-dim- Ey = (E₁cosθ + E₂cosθ)ŷ Ey = 2E₁cosθŷ E₁ = q/(4πε₀(y²+a²)) (equation labeled (y)) Section 1: Force and Oscillations force F = (-2q')(2q/(ππε₀(y²+a²))^(3/2))ŷ (equation labeled (e)) for S.H.M (ya) F = -2q'y/(2ππε₀a³)ŷ (equation labeled (5)) S.H.M force F = kyŷ Ky = 2q'/(ππε₀a³) (equation labeled (f)) ωy = √(2q'/(ππε₀a³m)) Section 2: Relationship between Force Constants |Ky| = |Kz| = (1/2)|Kxy| |Ky| = |Kz| = (1/2)|Kx|