# Eletricidade, Magnetismo e Circuitos

## Formulário

### 1. Campo elétrico

$F = \dfrac{k|q_1||q_2|}{K\;r^2}$
$E_\text{pontual} = \dfrac{k|q|}{K\;r^2}$
$\vec{E} = \dfrac{\vec{F}}{q_0}$

### 2. Voltagem e corrente

$V_\mathrm{A} - V_\mathrm{B} = \displaystyle\int_{\mathrm{A}}^{\mathrm{B}}E\,\mathrm{d} s$
$U_\mathrm{e} = q\,V\vphantom{\displaystyle\int}$
$\dfrac{m}{2}v^2 + q\,V = \dfrac{m}{2}v_0^2 + q\,V_0$
$I = \displaystyle\lim_{\Delta t\rightarrow 0}\dfrac{\Delta Q}{\Delta t}$
$\Delta Q = \displaystyle\int_{t_1}^{t_2} I\;\mathrm{d}t$
$P = \displaystyle\lim_{\Delta t\rightarrow 0}\dfrac{\Delta U_\mathrm{e}}{\Delta t}$
$P = I\,\Delta V\vphantom{\displaystyle\int}$
$P_\text{f.e.m.} = I\,\varepsilon\vphantom{\displaystyle\int}$

### 3. Resistência

$\Delta V = R\,I\vphantom{\displaystyle\int}$
$\Delta V_\text{gerador} = \varepsilon - r\,I\vphantom{\displaystyle\int}$
$\Delta V_\text{recetor} = \varepsilon + r\,I\vphantom{\displaystyle\int}$
$R = \rho\,\dfrac{L}{A}$
$R = R_{20}\left(1 + \alpha_{20}(T - 20)\right)\vphantom{\displaystyle\int}$
$R_\mathrm{s} = R_1+R_2\vphantom{\displaystyle\int}$
$R_\mathrm{p} = \dfrac{R_1\,R_2}{R_1 + R_2}$

$C_\text{condutor}=\dfrac{Q}{V_\text{sup}}$
$C = \dfrac{Q}{\Delta\,V}$
$V_\text{max} = E_\text{max}\,d$
$U = \dfrac{1}{2}\,Q\,\Delta V$
$C_\text{plano} = \dfrac{K\,A}{4\,\pi\,k\,d}$
$C_\mathrm{p} = C_1 + C_2$
$\dfrac{1}{C_\mathrm{s}} = \dfrac{1}{C_1} + \dfrac{1}{C_2}$

### 5. Circuitos de corrente contínua

$I_1 + \ldots + I_n = 0\vphantom{\displaystyle\int}$
$\Delta V_1 + \ldots + \Delta V_n = 0\vphantom{\displaystyle\int}$
$\displaystyle\sum_{j=1}^n R_{ij}\,I_j = \varepsilon_i \quad (i=1,\ldots,n)$

### 6. Fluxo elétrico

$\vec{E} = \displaystyle\sum_{i=1}^n\frac{k\,q_i (\vec{r}-\vec{r}_i)}{\left|\vec{r}-\vec{r}_i\right|^3}$
$\varPhi = A\,E\,\cos\theta\vphantom{\displaystyle\int}$
$\varPhi(\text{S fechada}) = 4\,\pi\,k\,q_{\text{int}}\vphantom{\displaystyle\int}$
$E_\mathrm{plano} = 2\,\pi\,k\,\sigma\vphantom{\displaystyle\int}$
$E_\text{fio} = \dfrac{2\,k\,\lambda}{R}$
$E_\text{esf} = \dfrac{kQ}{r^2}\quad (r>R)$

### 7. Potencial

$\mathrm{d} V = -\vec{E}\cdot \mathrm{d}\vec{r}\vphantom{\displaystyle\int}$
$E_s = -\dfrac{\mathrm{d}V}{\mathrm{d}s}$
$V = -\displaystyle\int_\infty^\mathrm{P} \vec{E}\cdot d\vec{r}$
$V = \displaystyle\sum_{i=1}^n\dfrac{k\,q_i}{|\vec{r}-\vec{r}_i|}$
$V_\text{esf} = \dfrac{kQ}{r}\quad (r>R)$

### 8. Campo magnético

$\vec{F} = L\;\vec{I}\times \vec{B}\vphantom{\displaystyle\int}$
$\vec{F} = q\,\left(\vec{E} + \vec{v}\times\vec{B}\right)\vphantom{\displaystyle\int}$
$\vec{M} = \vec{m}\times\vec{B}\vphantom{\displaystyle\int}$
$\vec{m} = A\,I\,\hat{n}\vphantom{\displaystyle\int}$
$r = \dfrac{m\,v}{q\,B}$
$\omega = \dfrac{q\,B}{m}$
$\displaystyle\oint_\mathrm{C} \vec{B}\cdot\mathrm{d}\vec{r} = 4\,\pi\,k_m\,I_\text{int}$
$B_\text{fio reto} = \dfrac{2\,k_\mathrm{m}\,I}{r}$
$F_\text{fios retos} = \dfrac{2\,k_\mathrm{m}\,L\, I_1\, I_2}{r}$
$\dfrac{\partial B_x}{\partial x} + \dfrac{\partial B_y}{\partial y} + \dfrac{\partial B_z}{\partial z} = 0$

### 9. Indução eletromagnética

$\vec{E}_\mathrm{i} = \vec{v}\times\vec{B}\vphantom{\displaystyle\int}$
$\varepsilon_i = L\,|\vec{v}\times\vec{B}|\vphantom{\displaystyle\int}$
$\varepsilon_i = -\dfrac{\mathrm{d}\varPsi}{\mathrm{d}t}$
$\varPsi = A\,B\,\cos\theta\vphantom{\displaystyle\int}$
$\varepsilon_i = -L\,\dfrac{\mathrm{d}I}{\mathrm{d}t}$

### 10. Processamento de sinais

$\tilde{V}(s) = Z(s)\;\tilde{I}(s)\vphantom{\displaystyle\int}$
$Z_{R} = R\vphantom{\displaystyle\int}$
$Z_{L} = L\,s\vphantom{\displaystyle\int}$
$Z_{C} = \dfrac{1}{C\,s}$
$Z_{\text{s}} = Z_1 + Z_2\vphantom{\displaystyle\int}$
$Z_{\text{p}} = \dfrac{Z_1Z_2}{Z_1+Z_2}$
$\tilde{V}(s) = H(s)\;\tilde{V}_e(s)\vphantom{\displaystyle\int}$

### 11. Circuitos de corrente alternada

$V = V_\text{max} \cos(\omega\,t + \varphi)\vphantom{\displaystyle\int}$
$\omega = 2\,\pi\,f \hspace{15pt} f = \dfrac{1}{T}$
$\mathbf{V} = Z(\mathrm{i}\,\omega)\,\mathbf{I}\vphantom{\displaystyle\int}$
$Z(\mathrm{i}\,\omega) = R(\omega) + \mathrm{i}\,X(\omega)\vphantom{\displaystyle\int}$
$\langle P \rangle = \dfrac{1}{2}\,V_\text{max}\,I_\text{max}\,\cos\varphi_Z$
$V_\mathrm{ef} = \dfrac{V_\text{max}}{\sqrt{2}} \qquad I_\mathrm{ef} = \dfrac{I_\text{max}}{\sqrt{2}}$
$\mathbf{V} = H(\mathrm{i}\,\omega)\,\mathbf{V}_e\vphantom{\displaystyle\int}$

### 12. Ondas eletromagnéticas e luz

$\varPhi(\text{S fechada}) = 4\,\pi\,k\,q_\text{int}\vphantom{\displaystyle\int}$
$\varPsi(\text{S fechada}) = 0\vphantom{\displaystyle\int}$
$\displaystyle\oint_\mathrm{C} \vec{E}\cdot\mathrm{d}\vec{r} = -\dfrac{\mathrm{d}\varPsi_\mathrm{C}}{\mathrm{d}t}$
$\displaystyle\oint_\mathrm{C} \vec{B}\cdot\mathrm{d}\vec{r} = 4\pi k_m I_\mathrm{C} + \dfrac{k_\mathrm{m}}{k}\dfrac{\mathrm{d}\varPhi}{\mathrm{d}t}$
$\dfrac{k_\mathrm{m}}{k} = \dfrac{1}{c^2}$
$\dfrac{\partial^2 E}{\partial t^2} = c^2\,\dfrac{\partial^2 E}{\partial y^2}$
$\dfrac{\partial^2 B}{\partial t^2} = c^2\,\dfrac{\partial^2 B}{\partial y^2}$
$B = \dfrac{E}{c}$
$\vec{E}\times\vec{B} \longrightarrow \vec{v}\vphantom{\displaystyle\int}$
$E = E_\text{max}\,\sin\left(\dfrac{2\pi\,x}{\lambda}-\omega\,t+\varphi\right)$
$c = \dfrac{\lambda}{T} = \lambda\,f$
$U = h\,f\vphantom{\displaystyle\int}$