Reference no: EM13979008
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.
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