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\HTML{TR}\HTML{TD}Legge di Coulomb\HTML{TD}$${\bf F}=k\frac{q_1 q_2}{r^2}\overline{{\bf r}} ; k=\frac{1}{4\pi\epsilon};[k]=\frac{N m^2}{C^2};=\frac{J m}{C^2}=\frac{V m}{C}=\frac{V}{C/m}=\frac{V}{\lambda};[\epsilon]=\frac{\lambda}{V};\epsilon=\epsilon_r \epsilon_0;k_0\approx9\times10^9 \frac{N m^2}{C^2};\epsilon_0\approx9\times10^{-12} \frac{C^2}{N m^2};F_m=\frac{F_0}{\epsilon_r}$$\\
$\epsilon_r: ambra=2.8 , silicio=12 , vetro=5-10 , acqua= 80 , aria=1.00056$
\HTML{TR}\HTML{TD}Campo elettrico\HTML{TD}$${\bf E}=\frac{{\bf F}}{q};{\bf E_{carica centrale}}=k\frac{q}{r^2}\overline{{\bf r}} ; [E]=\frac{J}{C m}=\frac{V}{m}$$
\HTML{TR}\HTML{TD}Principio di sovrapposizione\HTML{TD}$${\bf E}=\Sigma \textbf{E_i}$$
\HTML{TR}\HTML{TD}Densità di carica\HTML{TD}$$lineare: \lambda=\frac{Q}{l} , [\lambda]=\frac{C}{m}; superficiale: \sigma=\frac{Q}{S} , [\sigma]=\frac{C}{m^2}; (volumica): \rho=\frac{Q}{V} , [\rho]=\frac{C}{m^3}; $$
\HTML{TR}\HTML{TD}{\bf 1° Eq. Maxwell}: Teorema di Gauss \\(ovvero del flusso di {\bf E})\HTML{TD} $$\Phi({\bf E})=\frac{Q}{\epsilon} \ \ \ \ :  \left[ \Phi({\bf E}) = \int_S {{\bf E} \times {\bf dS}}=\sum_{( S )} E_i S_i cos \theta_i = \frac{Q_{interna S}}{\epsilon} \right]$$
\HTML{TR}\HTML{TD}Applicazioni:\HTML{TD}$$Esterno Sfera : E=\frac{Q}{4\pi\epsilon r^2};Esterno filo : E=\frac{\lambda}{2\pi\epsilon r};Piano infinito: E=\frac{\sigma}{2\epsilon}$$
\HTML{TR}\HTML{TD}Differenza di potenziale\HTML{TD}$$\Delta V=-\int_A^B{\bf E} {\bf dS} \ \ ;\ \  se uniforme  = -E (X-X_0) ; in campo radiale: \Delta V=\frac{q}{4\pi\epsilon}\left[ \frac{1}{r_b}-\frac{1}{r_a}\right] , [V]=\frac{J}{C} ; $$
\HTML{TR}\HTML{TD}Capacità\HTML{TD}$$C=\frac{Q}{V} ; C_{par}=\Sigma C_i ; C_{serie}=\frac{1}{\left(\Sigma \frac{1}{C_i}\right)} ; C_{serie 2 cap.}= \frac{C_1C_2}{C_1+C_2} ; C_{cond. piano}= \frac{Q}{V}=\frac{\sigma S}{E(X-X_0)}=\frac{\sigma S}{\frac{\sigma}{2\epsilon}(X-X_0)}=\frac{2\epsilon S}{d}; En_{cond piano}=\frac{1}{2}C\Delta V^2 $$
\HTML{TR}\HTML{TD}{\bf 1° Eq. Maxwell}: Teorema di Gauss \\(ovvero del flusso di {\bf E})\HTML{TD} $$\Phi({\bf E})=\frac{Q}{\epsilon} \ \ \ \ :  \left[ \Phi({\bf E}) = \int_S {{\bf E} \times {\bf dS}}=\sum_{( S )} E_i S_i cos \theta_i = \frac{Q_{interna S}}{\epsilon} \right]$$
\HTML{TR}\HTML{TD}{\bf 2° Eq. Maxwell}: (ovvero del flusso di {\bf B})\HTML{TD} $$\Phi({\bf B})= 0 $$
\HTML{TR}\HTML{TD}{\bf 3° Eq. Maxwell}: (Faraday Newman)\HTML{TD} $$C({\bf E})=-\frac{\Delta \Phi ({\bf B})}{\Delta t} \ \ : \ \int_{(circ. chiuso)} \left({{\bf E} \times {\bf dr}}\right) \ \ = \ \ \sum_{(circ.chiuso)} E_i r_i cos \theta_i $$
\HTML{TR}\HTML{TD}{\bf 4° Eq. Maxwell}: (Teo di Ampere)\HTML{TD} $$C({\bf B})=\mu_0 i + \mu_0 \epsilon_0 \frac{\Delta \Phi ({\bf E})}{\Delta t}$$
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