Page Description Equation
714 Coulomb. SI unit for charge. \[ \mathrm{C} \]
719
770		 SI units for electric field. \[ \vect{E}\left(\frac{\mathrm{N}}{\mathrm{C}}\right) \text{ or } \left(\frac{\mathrm{V}}{\mathrm{m}}\right), \ 1\frac{\mathrm{N}}{\mathrm{C}}=1\frac{V}{\mathrm{m}} \]
710
714		 proton charge $=e$, electron charge $=-e$; smallest isolated charge found in nature. \[ \left|e\right|=1.602\ 177\ 33\left(4\ 9\right)\times{10}^{-19}\mathrm{\ C} \]
714 number of electrons (or protons) in one coulomb of charge \[ 1\mathrm{C}\approx 6.24\times{10}^{18}e \]
710 electric charge is quantized \[ q=ne,\ \ \left(n\text{ an integer}\right) \]
714 permittivity of free space \[ \epsilon_0=8.854\ 2\times{10}^{-12}\frac{\mathrm{C}^2}{\mathrm{N}\cdot\mathrm{m}^2} \]
714 Coulomb constant \[ k_e=\frac{1}{4\pi\epsilon_0}=8.987\ 5\times{10}^9\mathrm{\ }\frac{\mathrm{N}\cdot \mathrm{m}^2}{\mathrm{C}^2} \]
714 charge on quarks \[ \frac{e}{3}\text{ or }2\frac{e}{3} \]
714 Coulomb's law. $F_e$ is the magnitude of electric force (aka Coulomb force). Compare with gravitational force $F_g.$ \[ F_e=k_e\frac{\left|q_1\right|\left|q_2\right|}{r^2} \]
715 electric force exerted by charge $q_1$ on $q_2$ where $\hat{\vect{r}}$ is the unit vector directed from $q_1$ to $q_2.$ \[ \vect{F}_{12}=k_e\frac{q_1q_2}{r^2}\hat{\vect{r}} \]
716 Newton's third law applied to electric forces \[ \vect{F}_{12}=-\vect{F}_{21} \]
716 electric force due to a system of charges on a charge $q_n.$ N.b. The force exerted by an electric field at a point depends on the charge at that point. \[ \vect{F}_n=\sum\vect{F}_{jn} \]
715 electric field at a point due to a point charge $q.$ $r$ is the distance between $q$ and the point. $\hat{\vect{r}}$ is the unit vector directed from $q$ to the point. N.b. $\vect{E}$ is independent of the test charge $q_0,$ it depends only on $q$ and $r.$ \[ \vect{E}\equiv\frac{\vect{F}_e}{q_0}=k_e\frac{q}{r^2}\hat{\vect{r}},\ \ \left(\vect{F}_\vect{e}\propto q_0\right) \]
728 electric force on a point charge $q$ due to electric field $\vect{E}.$ \[ \vect{F}_e=q\vect{E} \]
721 electric field at a point due to a finite system of charges. $r_i=$ distance between the point and the system charge $q_i.$ ${\hat{\vect{r}}}_i=$ unit vector directed from $q_i$ to the point. \[ \vect{E}=k_e\sum{\frac{q_i}{r_i^2}{\hat{\vect{r}}}_i} \]
723 electric field at a point due to a continuous charge distribution \[ \vect{E}=k_e\int{\frac{dq}{r^2}\hat{\vect{r}}} \]
723 linear charge density \[ \lambda=\frac{dQ}{dL}\ \ \ \left(\frac{\mathrm{C}}{\mathrm{m}}\right) \]
723 surface charge density \[ \sigma=\frac{dQ}{dA}\ \ \ \left(\frac{\mathrm{C\ }}{\mathrm{\ m}^2}\right) \]
723 volume charge density \[ \rho=\frac{dQ}{dV}\ \ \ \left(\frac{\mathrm{C\ }}{\mathrm{\ m}^3}\right) \]
722 electric field due to an electric dipole along the perpendicular line ($y$-axis) bisecting the line joining the two poles ($x$-axis) \[ \begin{align*} E&=k_e\frac{2qa}{\left(y^2+a^2\right)^{3/2}}\\ E&=k_e\frac{2qa}{y^3},\ \ \left(y\gg a\right) \end{align*} \]
722 electric field due to an electric dipole at great distances from the dipole along the line joining the two poles ($x$-axis) \[ E=k_e\frac{4qa}{x^3},\ \ \left(x\gg a\right) \]
724 electric field due to a uniformly charged rod of length $l$ and total charge $Q$ at a distance a along the rod's long axis \[ E=\frac{k_eQ}{a\left(l+a\right)} \]
724 electric field due to a uniformly charged ring of radius $a$ at a distance $x$ along the central axis perpendicular to the ring's plane \[ E=\frac{k_eQx}{\left(x^2+a^2\right)^3} \]
725 electric field due to a uniformly charged disk of radius $R$ and surface charge density $\sigma$ at a point along the central perpendicular axis located a distance $\abs{x}$ from the center of the disk. In deriving this formula, note that a) the integration is over a variable radius $r$ from $0$ to $R$, b) the result from example 23.8 is used, c) the formula $A=2\pi r\,dr$ for the area of a washer is used, d) unlike the previous examples, the result depends on the (surface) charge density. \[ \begin{align*} E&=\frac{\sigma}{2\epsilon_0}\left[\frac{x}{\abs{x}}-\frac{x}{\left(x^2+R^2\right)^{1/2}}\right],\ \left(x\geq0\right)\\ E&\approx\frac{\sigma}{2\epsilon_0}=2\pi k_e\sigma,\ \left(R\gg x\right) \end{align*} \]
727 number of field lines are proportional to charge \[ \frac{N_1}{N_2}=\frac{q_1}{q_2} \]
728 acceleration due to electric field $\mathrm{E}$ of charge $q_0$ with mass $m.$ \[ \vect{a}=\frac{\vect{F}_e}{m}=\frac{q_0\vect{E}}{m}\ \ \ \left(\frac{\mathrm{N}}{\mathrm{kg}}\right) \]

Notes

Page Notes
709 A positive charge is the charge a glass rod has when it is rubbed with silk.
709 A negative charge is the charge a rubber rod has when it is rubbed with fur.
711 Examples of conductors include copper, aluminum, silver.
711 Examples of insulators include glass, rubber, wood.
711 Examples of semiconductors include silicon, germanium.
714 A torsion balance is an instrument for verifying Coulomb's law
720 The electric field line of a point charge $q$ points radially outward if $q\gt 0,$ radially inward if $q\lt 0.$