Electric Field Formula
Objects with electric charge emit electric fields. This electric field is the source of the electrostatic force that nearby charged objects experience. The electric field is a vector quantity, and the direction of the field lines depends on the sign of the source charge. Electric field vectors point away from positively charged sources, and towards negatively charged sources. The formula for the electric field includes the Coulomb constant, which is \[k\cong 8.988 \times 10 N.m^{2}/C^{2} \] . The Coulomb constant can also be written in terms of the permittivity of free space,
. In that form, the Coulomb constant is \[k=1/4 \pi\varepsilon _{0} \] . The unit of the electric field magnitude is Newtons per Coulomb, N/C.
\[electric\: field = (coulomb \: constant)\frac{source\: charge}{(distance from the charge)^{2}}(direction vector) \]
\[\vec{E}=k\frac{q}{r^{2}}\hat{r} \]
\[\vec{E} \] = electric field vector at a certain position in space (N/C)
k = Coulomb constant ()
q = charge of a single point source of the electric field (C)
r = distance from the source charge (m)
\[ \vec{r} \] = unit vector (length is 1), the direction of the electric field (unitless)
