## Electric Fields

• ### Units and Variables

• q - charge, in coulombs
• Fe - force due to electric fields, in newtons
• ke - 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
• ${k}_{e}=\frac{1}{4\pi {\epsilon }_{0}}=8.9875×{10}^{9}\frac{N{m}^{2}}{{C}^{2}}$
• ${\epsilon }_{0}=8.8542×{10}^{-12}\frac{{C}^{2}}{N{m}^{2}}$
• $e=1.602×{10}^{-\mathrm{19}}C$
• ${F}_{e}={k}_{e}\frac{|{q}_{1}||{q}_{2}|}{{r}^{2}}$
• ${F}_{12}={k}_{e}\frac{{q}_{1}{q}_{2}}{{r}^{2}}\stackrel{^}{r}$
• $E\equiv \frac{{F}_{e}}{{q}_{0}}$
• $E={k}_{e}\frac{q}{{r}^{2}}\stackrel{^}{r}$
• $E={k}_{e}\underset{i}{\Sigma }\frac{q}{{r}_{i}^{2}}\stackrel{^}{r}$
• $E={k}_{e}\underset{i}{\overset{f}{\int }}\frac{\mathrm{dq}}{{r}^{2}}\stackrel{^}{r}$
• #### 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

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