How To Find the Electric Field for Simple Point Charges

If you have to find the electric field $\vec{E}$ rather than the force on a specific charge $q$, the procedure is very similar to finding the Coulomb force, except that you evaluate the electric field vector instead of the force vector.

1. Identify the spot $X$ where you want to find the field.
2. For each source charge $q_i$, draw the electric field vector $\vec{E}_{i}$ at $X$ due to $q_i$, remembering that direction of $\vec{E}$ is away from positive charges and towards negative ones. When considering the field due to $q_i$, ignore the presence of any other charges.
3. Find the magnitude of this field at $X$: $E_{i}=kq_i/r_i^2$, where $r_i$ is the distance from the source charge to the spot $X$ you're at.
4. Decompose the field into components in your chosen coordinate system.
5. Repeat for every other source charge in the problem.
6. Now add the fields $\vec{E}_{i}$ vectorially, i.e. add up the $\hat{i}$, $\hat{j}$ and $\hat{k}$ components. The resultant vector is the total electric field vector.