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

2024
Views:

40

Pages:

5
Author:

Jabin F.

# Poynting vector S = (E×B) / μ₀ ∴ (-E₀) × (-B₀) = +E₀B₀ S = (μ₀Po / 16π²r²c²) sin²θ cos²(ωt - ωr/c) r̂ (spherical wave) E(r, θ, ϕ, t) = (E₀ω²/c) sinθ cos(ωt - ωr/c) r̂ This is electric field of magnetic dipole (page-993) |E| = c E(r, θ, ϕ, t) = (E₀ω²/c) sinθ cos(ωt - ωr/c) r̂ ∴ S = (1/μ₀) E × B ⇒ r̂ = ϕ̂ × (-θ̂) \[\vec{S}=\frac{E_{0}^{2}\omega^{4}sin^{2}\theta}{4\pi\mu_{0}r^{2}c}cos^{2}[w(t-\frac{r}{c})]\hat{r}\] \[\vec{I}=\langle\vec{S}\rangle=\frac{E_{0}^{2}\omega^{4}sin^{2}\theta}{\mu_{0}r^{2}c}\frac{\pi}{2}\] \[\langle P\rangle=\int_{S}\vec{I}\cdot d\vec{a}=\int_{0}^{\pi}\int_{0}^{2\pi}\frac{E_{0}^{2}\omega^{4}sin^{2}\theta}{\mu_{0}r^{2}c}\cdot r^{2}sin\theta d\theta d\phi\] \[=\frac{E_{0}^{2}\omega^{4}}{4\pi\mu_{0}c}(\frac{4}{3})\] \[=\frac{4\pi E_{0}^{2}\omega^{4}}{3\mu_{0}c}\] (option-b) Plane Wave → \[\vec{E}=E_{0}\hat{x}sin(kz-wt)\] ↳ (In plane wave no position dependency) Ques.27 page-97 \[E\propto\frac{1}{r}\], \[B\propto\frac{1}{r}\] (option-c) Ques.29 page-97 \[I\propto P_{0}^{2}sin^{2}\theta\] ∴ \[P_{0}=I_{0}d\] ⇒ \[I\propto d^{2}sin^{2}\theta\] (option-c) Ques.24 Page-96 \[\vec{S}=\frac{1}{\omega\mu_{0}}\vec{E}\times\vec{B}\] \[E\propto\frac{1}{r^{n}}\] \[\overline{S}\propto\frac{1}{r^{m}}\] \[n=1, m=2\] (option-c) Ques.25 Page-96 \[E\propto r^{-n}\] \[B\propto r^{-m}\] , n=1, m=1 (option-c) Ques-95 Page-96 E, F, and m.F ∝ 1/r (option-a) Ques-23 Page-96 (i) Constant velocity → a=0 so PA=0 (ii) Circular motion a≠0, Pø≠0 (iii) Pc≠0