Chapter 23 Electric Fields
Page  Description  Equation 

714 

\[ \mathrm{C} \] 
719 770 

\[ \vect{E}\left(\frac{\mathrm{N}}{\mathrm{C}}\right) \text{ or } \left(\frac{\mathrm{V}}{\mathrm{m}}\right), \ 1\frac{\mathrm{N}}{\mathrm{C}}=1\frac{V}{\mathrm{m}} \] 
710 714 

\[ \lefte\right=1.602\ 177\ 33\left(4\ 9\right)\times{10}^{19}\mathrm{\ C} \] 
714 

\[ 1\mathrm{C}\approx 6.24\times{10}^{18}e \] 
710 

\[ q=ne,\ \ \left(n\text{ an integer}\right) \] 
714 

\[ \epsilon_0=8.854\ 2\times{10}^{12}\frac{\mathrm{C}^2}{\mathrm{N}\cdot\mathrm{m}^2} \] 
714 

\[ k_e=\frac{1}{4\pi\epsilon_0}=8.987\ 5\times{10}^9\mathrm{\ }\frac{\mathrm{N}\cdot \mathrm{m}^2}{\mathrm{C}^2} \] 
714 

\[ \frac{e}{3}\text{ or }2\frac{e}{3} \] 
714 

\[ F_e=k_e\frac{\leftq_1\right\leftq_2\right}{r^2} \] 
715 

\[ \vect{F}_{12}=k_e\frac{q_1q_2}{r^2}\hat{\vect{r}} \] 
716 

\[ \vect{F}_{12}=\vect{F}_{21} \] 
716 

\[ \vect{F}_n=\sum\vect{F}_{jn} \] 
715 

\[ \vect{E}\equiv\frac{\vect{F}_e}{q_0}=k_e\frac{q}{r^2}\hat{\vect{r}},\ \ \left(\vect{F}_\vect{e}\propto q_0\right) \] 
728 

\[ \vect{F}_e=q\vect{E} \] 
721 

\[ \vect{E}=k_e\sum{\frac{q_i}{r_i^2}{\hat{\vect{r}}}_i} \] 
723 

\[ \vect{E}=k_e\int{\frac{dq}{r^2}\hat{\vect{r}}} \] 
723 

\[ \lambda=\frac{dQ}{dL}\ \ \ \left(\frac{\mathrm{C}}{\mathrm{m}}\right) \] 
723 

\[ \sigma=\frac{dQ}{dA}\ \ \ \left(\frac{\mathrm{C\ }}{\mathrm{\ m}^2}\right) \] 
723 

\[ \rho=\frac{dQ}{dV}\ \ \ \left(\frac{\mathrm{C\ }}{\mathrm{\ m}^3}\right) \] 
722 

\[ \begin{align*} E&=k_e\frac{2qa}{\left(y^2+a^2\right)^{3/2}}\\ E&=k_e\frac{2qa}{y^3},\ \ \left(y\gg a\right) \end{align*} \] 
722 

\[ E=k_e\frac{4qa}{x^3},\ \ \left(x\gg a\right) \] 
724 

\[ E=\frac{k_eQ}{a\left(l+a\right)} \] 
724 

\[ E=\frac{k_eQx}{\left(x^2+a^2\right)^3} \] 
725 

\[ \begin{align*} E&=\frac{\sigma}{2\epsilon_0}\left[\frac{x}{\abs{x}}\frac{x}{\left(x^2+R^2\right)^{1/2}}\right],\ \left(x\geq0\right)\\ E&\approx\frac{\sigma}{2\epsilon_0}=2\pi k_e\sigma,\ \left(R\gg x\right) \end{align*} \] 
727 

\[ \frac{N_1}{N_2}=\frac{q_1}{q_2} \] 
728 

\[ \vect{a}=\frac{\vect{F}_e}{m}=\frac{q_0\vect{E}}{m}\ \ \ \left(\frac{\mathrm{N}}{\mathrm{kg}}\right) \] 
Notes 

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A

720 
