Notes on E&M
Notes on E&M Definitions E ⃗ = F ⃗ q \vec E = \frac{\vec F}{q} E = q F ϕ E = ∫ E ⃗ ⋅ d A ⃗ \phi_E = \int \vec E \cdot d\vec A ϕ E = ∫ E ⋅ d A ϕ B = ∫ B ⃗ ⋅ d l ⃗ \phi_B = \int \vec B \cdot d\vec l ϕ B = ∫ B ⋅ d l ε = ∮ L F ⃗ o n c h a r g e q q ⋅ d l ⃗ \varepsilon = \oint_{L} \frac{\vec F_{on \, charge \, q}}{q} \cdot d\vec l ε = ∮ L q F o n c h a r g e q ⋅ d l Δ V = − ∫ A B E ⃗ ⋅ d l ⃗ \Delta V = -\int^B_A \vec E \cdot d\vec l Δ V = − ∫ A B E ⋅ d l if ∮ L E ⃗ ⋅ d l ⃗ = 0 \oint_L\vec E \cdot d\vec l= 0 ∮ L E ⋅ d l = 0 E ⃗ \vec E E created by charges Maxwell’s Equations Gauss’s Law ∮ E ⃗ ⋅ d A ⃗ = q e n c l o s e d ε 0 \oint \vec E \cdot d \vec A = \frac{q_{enclosed}}{\varepsilon_0} ∮ E ⋅ d A = ε 0 q e n c l o s e d → charges make E ⃗ \vec E E , which is path-independent ∮ B ⃗ ⋅ d A ⃗ = 0 \oint \vec B \cdot d \vec A = 0 ∮ B ⋅ d A = 0 → there is ...