Review

Equations

$F_{e} = k_{e}\cdot\frac{|q_{1}|\cdot|q_{2}|}{r^{2}}$ $F_{e} = k_{e} \cdot \frac{∣ q _{1} ∣ \cdot ∣ q _{2} ∣}{r ^{2}}$
- $F_{e}$ = electric force
- $k_{e}$ = Coulomb's constant
- $q_{1}$ and $q_{2}$ = the two charges
- $r$ = distance between the charges

$\mathbf{E} = \frac{\mathbf{F}_{e}}{q_{0}}$ $E = \frac{F _{e}}{q _{0}}$
- $\mathbf{E}$ = the electric field vector
- $\mathbf{F}_{e}$ = the electrical force
- $q_{1}$ and $q_{2}$ = the two charges
- $q_{0}$ = the positive test charge
$\mathbf{F}_{e} = q\mathbf{E}$ $F_{e} = q E$
- Alternate form of the equation above

$\mathbf{E} = k_{e}\frac{q}{r^{2}}\mathbf{\hat{r}}$ $E = k_{e} \frac{q}{r ^{2}} \hat{r}$
- $k_{e}$ = Coulomb's constant
- $q$ = the magnitude of force between the point charge ( $q$ ) and the test charge
- $r^{2}$ = the distance between the point charge ( $q$ ) and the point of interest
$\mathbf{E} = k_{e}\sum_{i}^{}\frac{q_{i}}{r^{2}_{i}}\hat{\mathbf{r}}_{i}$ $E = k_{e} \sum_{i} \frac{q _{i}}{r _{i}^{2}} \hat{r}_{i}$ .
- $r_{i}$ = the distance between the $i$ th source charge $q_{i}$ and point $P$
- $\hat{\mathbf{r}}_{i}$ = a unit vector directed from $q_{i}$ toward $P$
- All other variables are the same as the equation above

Charge density formulas:
- Volume: $dq = \rho dV$
- Surface: $dq = \sigma dV$
- Line: $dq = \lambda dV$

$\mathbf{N} = \mathbf{C} q$ $N = C q$
- $\mathbf{N}$ = the number of lines
- $\mathbf{q}$ = the charge
- $\mathbf{C}$ = a constant

For ALL equations listed above:
- $q$ = the charge
- $\mathbf{E}$ = the electric field
- $m$ = the mass of the charge (sometimes listed as $m_{e}$ )

For ALL equations listed above:
- $q$ = the charge
- $\mathbf{E}$ = the electric field

$\Phi_E = EA_{\perp} = EAcos(\theta)$ $Φ_{E} = E A_{⊥} = E A cos (θ)$
- $A_{\perp}$ = the area perpendicular to the electric field vectors
- $E$ = the electric field
- $\theta$ = the angle between the electric field line and an imaginary line that is perpendicular to the area
$\Phi_E = \oint \mathbf{E} \cdot d\mathbf{A}$ $Φ_{E} = \oint E \cdot d A$
- Note: you most likely won't have to worry about this equation. Most problems don't need this difficult calculus, so you can often use the easier formula listed below.
- $\oint \mathbf{E}$ = the surface integral of where the field is being produced/emitted
$\Phi_E = \frac{q}{\varepsilon_0}$ $Φ_{E} = \frac{q}{ε _{0}}$
- $q$ = the electric charge
- $\varepsilon_0$ = permittivity of free space

$k_{e} = 8.9875 \times 10^{9} \text{ N} \cdot \text{m}^{2}/\text{C}^{2} = \frac{1}{4\pi\epsilon_{0}}$ $k_{e} = 8.9875 \times 1 0^{9} N \cdot m^{2} / C^{2} = \frac{1}{4 π ϵ _{0}}$
- Coulomb's Constant
$\epsilon_{0} = 8.8542 \times 10^{-12} \text{ C}^{2} / \text{ N} \cdot \text{m}^{2}$ $ϵ_{0} = 8.8542 \times 1 0^{- 12} C^{2} / N \cdot m^{2}$
- Permittivity of free space in a vacuum