7.4 Determining Field from Potential

Which coordinate system would you use to calculate the electric field of a dipole?

If the electric field is zero throughout a region, must the electric potential also be zero in that region?

Throughout a region, equipotential surfaces are given by $z = \text{constant}$. The surfaces are equally spaced with $V = 100 \text{V}$ for $z = 0.00 \text{m}, V = 200 \text{V}$ for $z = 0.50 \text{m}, V = 300 \text{V}$ for $z = 1.00 \text{m}.$ What is the electric field in this region?

Calculate the electric field of an infinite line charge, throughout space.