Suppose the following function describes the electric potential on the xy plane:

V(x,y)=x² - y² + 1

(Units omitted; you may assume [x], [y] = m and [V] = V.)

a.) Find a general function E^→(x,y) and then use it to find the electric field at points A-D, which are at the indicated (x,y) coordinates:

Point A: E^→(+4 m,+3 m) = ____ N/C i^ + _____ N/C 

Point B: E^→(+4 m,-3 m) = _______ N/C i^ + _______ N/C 

Point C: E^→(-4 m,+3 m) = ______ N/C i^ + ______ N/C 

Point D: E^→(-4 m,-3 m) = ______ N/C i^ + _______ N/C 

Sketch the xy plane with the local fields you found indicated at their respective locations. Then answer:

What is the common electric potential at all of the coordinates listed above?

b.) An object (point mass m=3 kg, q=+6 C) is now placed at the origin.

What is the voltage at the origin?

How much energy does the object store here?

c.) The object is given an ever-so-slight nudge in the -y direction.

Use your electric field function to show that the object will always feel a force that points along the -y axis.

When the object arrives at y=-2 m, find:

The voltage at this location.
The energy stored by the object.
Its speed.