Eletromagnetismo e Circuitos

Formulário de Eletromagnetismo e Circuitos

{\vec{F}}_{j i} = \frac{k q_{j} q_{i}}{r_{j / i}^{2}} {\hat{r}}_{j / i}

\vec{F} = q \vec{E}

\vec{E} (\vec{r}) = \frac{k q}{r^{2}} \hat{r}

\vec{E} (\vec{r}) = k \sum_{i = 1}^{N} \frac{q_{i} (\vec{r} - {\vec{r}}_{i})}{{| \vec{r} - {\vec{r}}_{i} |}^{3}}

\vec{E} (\vec{r}) \approx k \int_{C} \frac{\vec{r} - {\vec{r}}^{'}}{{| \vec{r} - {\vec{r}}^{'} |}^{3}} λ ({\vec{r}}^{'}) d s^{'}

\vec{E} (\vec{r}) = k \iint_{S} \frac{\vec{r} - {\vec{r}}^{'}}{{| \vec{r} - {\vec{r}}^{'} |}^{3}} σ ({\vec{r}}^{'}) d A^{'}

Ψ_{S} = \iint_{S} \vec{E} \cdot d \vec{A}

∯_{S} \vec{E} \cdot d \vec{A} = 4 π k q_{int}

{\vec{E}}_{plano} = 2 π k σ \hat{n}

{\vec{E}}_{fio} (ϱ) = \frac{2 k λ}{ϱ} \hat{ϱ}

\frac{\partial E_{x}}{\partial y} = \frac{\partial E_{y}}{\partial x}

\frac{\partial E_{x}}{\partial z} = \frac{\partial E_{z}}{\partial x}

\frac{\partial E_{y}}{\partial z} = \frac{\partial E_{z}}{\partial y}

V = \frac{k q}{r}

V_{Q} - V_{P} = - \int_{P}^{Q} \vec{E} \cdot d \vec{r}

\vec{E} = - \vec{\nabla} V

V (\vec{r}) = \sum_{i = 1}^{N} \frac{k q_{i}}{| \vec{r} - {\vec{r}}_{i} |}

U_{e} = q V

Δ E_{c} + Δ E_{p} = W_{nc}

E_{c} = \frac{1}{2} m v^{2}

γ = \frac{1}{\sqrt{1 - v^{2} / c^{2}}}

γ = 1 + \frac{E_{c}}{m c^{2}}

U_{e} (r) = \frac{k q_{1} q_{2}}{r}

C_{condutor} = \frac{Q}{V} C = \frac{K Q}{Δ V}

U_{e} = \frac{1}{2} \frac{Q^{2}}{C} = \frac{1}{2} C Δ V^{2}

C_{plano} = \frac{K A}{4 π k d}

C_{esférico} = \frac{K a b}{k (b - a)}

\frac{1}{C_{s}} =

\frac{1}{C_{1}} + \frac{1}{C_{2}} + \dots + \frac{1}{C_{n}}

C_{p} = C_{1} + C_{2} + \dots + C_{n}

| I | = \frac{| Δ Q |}{Δ t}

Δ Q = \int_{t_{1}}^{t_{2}} I (t) d t

J = | ρ | v = \frac{I}{A}

\vec{J} = ρ \vec{v}

P = Δ V I

P = ε I

R = ρ_{e} \frac{ℓ}{A}

Δ V = R I

P = R I^{2} = \frac{Δ V^{2}}{R}

R = R_{20} [1 + α_{20} (T - 20)]

Δ V_{gerador} = ε - r I

Δ V_{recetor} = ε + r I

R_{s} = R_{1} + R_{2} + \dots + R_{N}

\frac{1}{R_{p}} = \frac{1}{R_{1}} + \frac{1}{R_{2}} + \dots + \frac{1}{R_{N}}

R_{p} = \frac{R_{1} R_{2}}{R_{1} + R_{2}}

R_{i} = \frac{R_{i j} R_{i k}}{R_{12} + R_{23} + R_{13}}

Δ V_{i} = \frac{R_{i}}{R_{s}} Δ V

I_{j} = \frac{R_{p}}{R_{j}} I

{\vec{F}}_{m} = q (\vec{v} \times \vec{B})

\vec{F} = q (\vec{E} + \vec{v} \times \vec{B})

{\vec{F}}_{m} = ℓ \vec{I} \times \vec{B}

ω = \frac{| q | B}{m}

r = \frac{v_{⟂}}{ω} = \frac{m v_{⟂}}{| q | B}

\vec{M} = \vec{m} \times \vec{B}

\vec{m} = I A \hat{n}

\vec{B} (\vec{r}) = k_{m} \int_{P}^{Q} \frac{\vec{I} \times (\vec{r} - {\vec{r}}^{'})}{{| \vec{r} - {\vec{r}}^{'} |}^{3}} d s^{'}

{\vec{B}}_{fio inf.} (ϱ) = \frac{2 k_{m} I}{ϱ} \hat{ϕ}

\oint_{C} \vec{B} \cdot d \vec{r} = 4 π k_{m} I_{C}

B_{sol. inf.} = 4 π k_{m} n I

\frac{F_{21}}{l} \approx \frac{2 k_{m} I_{1} I_{2}}{d}

{\vec{E}}_{i} = \vec{v} \times \vec{B}

ε_{i} = l | \vec{v} \times \vec{B} |

Φ_{S} = \iint_{S} \vec{B} \cdot d \vec{A}

ε_{i} = - \frac{d Φ}{d t}

ε_{i} = - L \frac{d I}{d t}

Δ V = L \frac{d I}{d t}

I_{d} = \frac{1}{4 π k} \iint_{S} \frac{\partial \vec{E}}{\partial t} \cdot d \vec{A}

V (t) = V_{máx} \cos (ω t + φ)

𝐕 = Z 𝐈

Z = R (ω) + i X (ω)

V_{máx} = | Z | I_{máx}

φ_{V} = φ_{Z} + φ_{I}

Z_{R} = R

Z_{C} = \frac{1}{i ω C} = \frac{1}{ω C} ∠ - \frac{π}{2}

Z_{L} = i ω L = ω L ∠ \frac{π}{2}

Z_{s} = Z_{1} + Z_{2}

Z_{p} = \frac{Z_{1} Z_{2}}{Z_{1} + Z_{2}}

V_{e f} = \frac{V_{máx}}{\sqrt{2}}

I_{e f} = \frac{I_{máx}}{\sqrt{2}}

\bar{P} = \frac{1}{2} V_{máx} I_{máx} \cos φ_{Z}

𝐕_{out} = ℛ (ω) 𝐕_{in}

\vec{\nabla} \cdot \vec{E} = 4 π k ρ

\vec{\nabla} \cdot \vec{B} = 0

\vec{\nabla} \times \vec{E} = - \frac{\partial \vec{B}}{\partial t}

\vec{\nabla} \times \vec{B} = 4 π k_{m} \vec{J} + \frac{k_{m}}{k} \frac{\partial \vec{E}}{\partial t}

c^{2} = \frac{k}{k_{m}}

Unidade de carga elementar	$e = 1.602 \times 10^{- 19}$ C
Constante de Coulomb	$k = 8.988 \times 10^{9} \frac{N \cdot m^{2}}{C^{2}}$
Constante magnética	$k_{m} = 10^{- 7} \frac{N}{A^{2}}$
Velocidade da luz no vácuo	$c = 2.998 \times 10^{8}$ m/s
Massa do eletrão	$m_{e} = 9.109 \times 10^{- 31}$ kg
Massa do protão	$m_{p} = 1.673 \times 10^{- 27}$ kg
Aceleração padrão da gravidade	$g = 9.807 \frac{m}{s^{2}}$