# Formulário Eletromagnetismo

| Número | Fórmula | Observação |
|:------:|:------------------------------------------------------------------------------------------------------------------------------------------------:|:----------:|
| 1 | $Q=\frac{f_{0}}{\Delta f}$ | |
| 2 | $\beta_{mn}=\sqrt{k^{2}-\left(\frac{m\pi}{a}\right)^{2}-\left(\frac{n\pi}{b}\right)^{2}}$ | |
| 3 | $k=\omega\sqrt{\mu \epsilon}$ | |
| 4 | $\beta_{mn}=\frac{l\pi}{d}$ | |
| 5 | $k_{mnl}=\sqrt{\left(\frac{m\pi}{a}\right)^{2}+\left(\frac{n\pi}{b}\right)^{2}+\left(\frac{l\pi}{d}\right)^{2}}$ | |
| 6 | $f_{mnl}=\frac{c}{2\pi\sqrt{\mu\epsilon}}\sqrt{\left(\frac{m\pi}{a}\right)^{2}+\left(\frac{n\pi}{b}\right)^{2}+\left(\frac{l\pi}{d}\right)^{2}}$ | |
| 7 | $Q=\omega\frac{W_{m}+W_{e}}{P}$ | |
| 8 | $W_{\epsilon}=\frac{\epsilon abd}{16}E_{0}^{2}$ | |
| 9 | $W_{m}=\frac{\epsilon abd}{16}E_{0}^{2}$ | |
| 10 | $R_{s}=\sqrt{\frac{\omega\mu}{2\sigma_{c}}}$ | |
| 11 | $\eta'=\sqrt{\frac{\mu}{\epsilon}}$ | |
| 12 | $P_{c}=\frac{R_{s}E_{0}^{2}\lambda^{2}}{8\eta'^{2}}\left(\frac{l^{2}ab}{d^{2}}+\frac{bd}{a^{2}}+\frac{l^{2}a}{2d}+\frac{d}{2a}\right)$ | |
| 13 | $Q_{c}=\frac{\left(kad\right)^{3}b\eta'}{2\pi^{2}R_{s}\left(2l^{2}a^{3}b+2bd^{3}+l^{2}a^{3}d+ad^{3}\right)}$ | |
| 14 | $Q_{d}=\frac{\epsilon'}{\epsilon''}$ | |
| 15 | $Q_{d}=\frac{1}{\tan\delta}$ | |
| 16 | $Q_{t}=\left(Q_{c}^{-1}+Q_{d}^{-1}\right)^{-1}$ | |
| 17 | $f_{mnl}=\frac{c}{2\pi\sqrt{\mu\epsilon}}\sqrt{\left(\frac{m\pi}{a}\right)^{2}+\left(\frac{n\pi}{b}\right)^{2}+\left(\frac{l\pi}{d}\right)^{2}}$ | d isolado |
| 18 | $f_{mnl}=\frac{c}{2\pi\sqrt{\mu\epsilon}}\sqrt{\left(\frac{m\pi}{a}\right)^{2}+\left(\frac{n\pi}{b}\right)^{2}+\left(\frac{l\pi}{d}\right)^{2}}$ | a isolado |
| 19 | $f_{mnl}=\frac{c}{2\pi\sqrt{\mu\epsilon}}\sqrt{\left(\frac{m\pi}{a}\right)^{2}+\left(\frac{n\pi}{b}\right)^{2}+\left(\frac{l\pi}{d}\right)^{2}}$ | b isolado |
| 20 | $\beta_{mn}=\sqrt{k^{2}-\left(\frac{\rho'_{nm}}{a}\right)^{2}}$ | |
| 21 | $f_{mnl}=\frac{c}{2\pi\sqrt{\mu\epsilon}}\sqrt{\left(\frac{\rho_{nm}}{a}\right)^{2}+\left(\frac{l\pi}{d}\right)^{2}}$ | |
| 22 | $\frac{d}{a}=2.03$ | |
| 23 | $P_{c}=\frac{R_{s}}{2}\pi H_{0}^{2}J_{n}^{2}\left(\rho'_{nm}\right)\left\{\frac{da}{2}\left[1+\left(\frac{\beta an}{\left(\rho'_{nm}\right)^{2}}\right)^{2}\right]+\left(\frac{\beta a^{2}}{\rho'_{nm}}\right)\left(1-\frac{n^{2}}{\left(\rho'_{nm}\right)^{2}}\right)\right\}$ | |
| 24 | $Q_{c}=\frac{\left(ka\right)^{3}\eta'ad}{4\left(\rho'_{nm}\right)^{2}R_{s}}\frac{\left[1-\left(\frac{n}{\rho'_{nm}}\right)^{2}\right]}{\left\{\frac{ad}{2}\left[1+\left(\frac{\beta an}{\left(\rho'_{nm}\right)^{2}}\right)^{2}\right]+\left(\frac{\beta a^{2}}{\rho'_{nm}}\right)\left(1-\frac{n^{2}}{\left(\rho'_{nm}\right)^{2}}\right)\right\}}$ | |
| 25 | $P_{d}=\frac{\omega\epsilon''k^{2}\eta'^{2}a^{4}H_{0}^{2}}{8\left(\rho'_{nm}\right)^{2}}\left[1-\left(\frac{n}{\rho'_{nm}}\right)^{2}\right]J_{n}^{2}\left(\rho'_{nm}\right)$ | |
| 26 | $Q_{c}=\frac{2.4049\sqrt{\frac{\mu}{\epsilon}}}{2\left(1+\frac{a}{d}\right)R_{s}}$ | |
| 27 | $k=\frac{2\pi f_{011}\sqrt{\epsilon_{r}}}{c}$ | |
| 28 | $\omega=2\pi f$ | |
| 29 | $f_{mnl}=\frac{c}{2\pi\sqrt{\mu\epsilon}}\sqrt{\left(\frac{\rho_{nm}}{a}\right)^{2}+\left(\frac{l\pi}{d}\right)^{2}}$ | d isolado, a=zd |
| 30 | $\sigma=\frac{ωϵ_{r}ϵ}{\tanδ}$ | |
| 31 | $\Delta f=2\left(f_{0}-f^{-}\right)$ | |
| 32 | $\frac{2a}{d}$ | |
| 33 | $Q_{c}=\left(Q_{t}^{-1}-Q_{d}^{-1}\right)^{-1}$ | |
| 34 | $R_{s}=x\frac{\pi\cdot\eta}{Q_{c}},\ \sigma_{c}=\frac{ωμ_{0}}{2R_{s}^{2}}$ | |
| 35 | $ϵ''=\frac{\sigma_{c}}{ω}$ | |
| 36 | $Q_{c}=\frac{\left(kad\right)^{3}b\eta'}{2\pi^{2}R_{s}\left(2l^{2}a^{3}b+2bd^{3}+l^{2}a^{3}d+ad^{3}\right)}$ | isola a, a=b=c |
| 37 | $f_{mnl}=\frac{c}{2\pi\sqrt{\mu\epsilon}}\sqrt{\left(\frac{m\pi}{a}\right)^{2}+\left(\frac{n\pi}{b}\right)^{2}+\left(\frac{l\pi}{d}\right)^{2}}$ | isola a, a=b=c |
| 38 | $Q_{c}=\frac{\left(kad\right)^{3}b\eta'}{2\pi^{2}R_{s}\left(2l^{2}a^{3}b+2bd^{3}+l^{2}a^{3}d+ad^{3}\right)}$ | isola $R_s$ |
| 39 | $R_{s}=\sqrt{\frac{\omega\mu}{2\sigma_{c}}}$ | isola $\sigma_{c}$|

## Condutividades

| Metal | Condutividade Elétrica $(\Omega m)^{-1}$ |
| ------------------ |:----------------------------------------:|
| Prata | $6.8\cdot10^{7}$ |
| Cobre | $6.0\cdot10^{7}$ |
| Ouro | $4.3\cdot10^{7}$ |
| Alumínio | $3.8\cdot10^{7}$ |
| Latão(70 Cu-30 Zn) | $1.6\cdot10^{7}$ |
| Ferro | $1.0\cdot10^{7}$ |
| Platina | $0.94\cdot10^{7}$ |
| Aço-carbono | $0.6\cdot10^{7}$ |
| Aço inoxidável | $0.2\cdot10^{7}$ |

## Valores correspondentes modo TE

| | $\rho'_{n0}$ | $\rho'_{n1}$ | $\rho'_{n2}$ | $\rho'_{n3}$ |
|:---:|:------------:|:------------:|:------------:|:------------:|
| n=0 | 0 | 3.832 | 7.016 | 10.174 |
| n=1 | 0 | 1.841 | 5.331 | 8.536 |
| n=0 | 0 | 3.054 | 6.706 | 9.970 |

## Valores correspondentes modo TM

| | $\rho_{n0}$ | $\rho_{n1}$ | $\rho_{n2}$ | $\rho_{n3}$ |
|:---:|:------------:|:------------:|:------------:|:------------:|
| n=0 | - | 2.405 | 5.520 | 8.654 |
| n=1 | 0 | 3.832 | 7.016 | 10.174 |
| n=0 | 0 | 5.135 | 8.417 | 11.620 |

###### tags: `UFBA`

###### tags: `UFBA`