At a particular location, the electric field points due north. (a) In what direction(s) will the rate of change of potential be greatest? (b) In what direction(s) will the rate of change of potential be least?

a) The biggest change is in the North direction towards the south

b)   the lowest exchange rate is in the esast -west where the change is zero

Explanation:

The field and the electric potential are related

          ΔV = - E ds

In the direction that the field increases the potential decreases

If the electro field points to the north, the potential must have an opposite behavior, or it must decrease towards the North.

Let's apply these deductions to the exercise.

a) The potential is greater towards the SOUTH

Therefore the biggest change is in the North direction towards the south

b) the lowest exchange rate is in the east- west where the change is zero

it about 600 mph from what i calculated