Using only what you know about the relationship of charges to electrostatic electric fields, namely: $$\EE=\frac{1}{4\pi\epsilon_0} \, \frac{Q\hat{r}}{r^2}$$ and the superposition principle, sketch the electric field (the vector field) for each of the following static charge configurations:

• Four positive charges arranged in a square.
• Two positive charges and two negative charges arranged in a square, with like charges diagonally opposite each other.
• A line segment with constant charge density.
• A circular loop with constant charge density.

Now, you should repeat this activity in two other ways:

1. Sketch the level curves for the electrostatic potential (see §Visualization of Potentials) and then visually/geometrically take the gradient.
2. Draw electric field lines for these charge configurations.

It would be useful for you to stop and think about which properties of the electric field are best repesented by the vector representation of the field and which by electric field lines.