Electrostatics

You should know how to finding forces ($\vec{F}$), potential energies (U), electric fields ($\vec{E}$) and electric potentials (V) by superposition (note that $\vec{F}=q\vec{E}$ and U=qV). For point charges we sum; for continuous charge distributions the sum becomes an integral. The basic laws are the electric field and electric potential due to a point charge,

$$\vec{E}={\frac{KQ\hat{r}}{r^{2}}=\frac{KQ\vec{r}}{r^{3}}},\ \ \ \ V={\frac{KQ% }{r}}.$$ (1)

where $K\sim 8.99\times 10^{9}$ Nm²/C² in MKS units and $\hat{r}$ is a unit vector in the radial direction. From these, along with superposition, everything can be derived. Note that $\vec{E}=-\vec{\nabla}V$.
 

• Sample problem: Summing effects of several sources
• Sample problem: Integrating effects of a continuous source