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

2024
Views:

460

Pages:

5
Author:

Jabin F.

Equation of Motion: m * dv/dt = -q^2 / (16 * pi * tau * epsilon_o * z^2) mv * dv/dt = -q^2 / (16 * pi * epsilon_o * z^2) * (dz/dt) d/dt (v^2/2) = +q^2 / (16 * pi * epsilon_o) * d/dt (1/z) mv^2/2 = q^2 / (16 * pi * epsilon_o * z) + C at z = d, v = 0 C = -q^2 / (16 * pi * epsilon_o * d) v^2 = (q^2 / (8 * pi * epsilon_o * m)) * (1/z - 1/d) dz/dt = ... integral from d to 0 dz = integral from 0 to t dt A horizontal line with points labeled D, C, A, and 0. Arrows indicating directions. Distances labeled -22, -4.5, -4.5, and 22. A vertical line with points labeled 1.5 and -1.5. Equation: F = +2(E)net F = +2(4pi * epsilon_o) * [(29 * (2 - 1)) / 1 + (2 * (2 + 1)) / 1 + 2 * (-2) / 4] F = 2 / (4pi * epsilon_o) * 792 * (-2) Annotation: Ques.47. No. of image charges n = (-360 - 1) m = odd no. and fraction not possible Table of Values: if θ = 0° => n = ∞ θ = 30° => n = 11 θ = 45° => n = 7 θ = 60° => n = 5 θ = 72° => n = 4 (not allowed) θ = 90° => n = 3 θ = 120° => n = 2 Equations: from eqn (i) V = dz/dt = q^2 / (8 * pi * epsilon_o * m) * (1/z - 1/d) dz/dt = A * (d - z) / (z * d)^(1/2) A = q^2 / (8 * pi * epsilon_o * m) ∫(z * d)^(1/2) / (d - z) dz = A ∫ dt Equation: d^(3/2) * [sin^(-1)(z/d) - (z/d)^2 * sqrt(1 - (z/d)^2)] = At + C Calculations: At time t = 0, z = d d^(3/2) * [sin^(-1)(1) - 1] = A(0) + C C = d^(3/2) * sin^(-1)(1) C = d^(3/2) * (π/2) time t = t when z = 0 d^(3/2) * [sin^(-1)(0) - 0] = At + d^(3/2) * (π/2) 0 = At + d^(3/2) * (π/2) At = -d^(3/2) * (π/2) A = -d^(3/2) * (π/2) * sqrt(q^2 / (8 * pi * epsilon_o * m)) t = -d^(3/2) * (π/2) * sqrt(8 * pi * epsilon_o * m / q^2) t = -8 * epsilon_o * m * d^(3/2) * (π/2) / q^2