Electric fields

Electric Fields

• Units and Variables

  • q - charge, in coulombs
  • F_e - force due to electric fields, in newtons
  • k_e - Coulomb Force Constant, in newton-meters squared per coulomb squared
  • ε₀ - Permittivity of free space, in coulomb squared per newton-meters squared
  • e - charge of an electron, in coulombs
  • E - electric field vector
  • ρ - volume charge density, in coulombs per meters cubed
  • σ - surface charge density, in coulombs per meters squared
  • λ - linear charge density, in coulombs per meter
  • Q - total charge of an electric field, in coulombs
• $k_e=\frac{1}{4\pi {\epsilon }_0}=8.9875\times {10}^9\frac{N{m}^2}{C^2}$
• ${\epsilon }_0=8.8542\times {10}^{-12}\frac{C^2}{N{m}^2}$
• $e=1.602\times {10}^{-\mathrm{19}}C$
• $F_e=k_e\frac{\left|q_1\right|\left|q_2\right|}{r^2}$
• $F_{12}=k_e\frac{q_1{q}_2}{r^2}\hat{r}$
• $E\equiv \frac{F_e}{q_0}$
• $E=k_e\frac{q}{r^2}\hat{r}$
• $E=k_e\underset{i}{\Sigma }\frac{q}{r_i^2}\hat{r}$
• $E=k_e\underset{i}{\overset{f}{\int }}\frac{\mathrm{dq}}{r^2}\hat{r}$

• Volume of Charge

  • $\rho \equiv \frac{Q}{V}$
  • $\mathrm{dq}=\rho \mathrm{dV}$

• Area of Charge

  • $\sigma \equiv \frac{Q}{A}$
  • $\mathrm{dq}=\sigma \mathrm{dA}$

• Line of Charge

  • $\lambda \equiv \frac{Q}{\ell }$
  • $\mathrm{dq}=\lambda \mathrm{d\ell }$
• $a=\frac{qE}{m}$