SP212/3321&5521
Chapter 24 - Worksheet #3
Question 1: The electric potential in some region is given by V (x, y) = 2x2 − 6xy − y 2 , where V has
units of volts when x and y have units of meters. (a) What is the electric field at the position (x, y)
~ = ~0)?
= (1 m, 2 m) in vector form? (b) At what position is the electric field zero (E
Question 2: Four point charges are arranged as shown at the corners of a square that is 0.65 m
on a side. What is the electric potential energy of the charges in this configuration? (Define the
potential energy to be zero when the charges are infinitely far apart.)
−2.00 µC
+2.00 µC
d=0.650 m
+2.00 µC
−2.00 µC
SP212/3321&5521
Chapter 24 - Worksheet #3
Question 3: Two point charges, each of +3.0 µC, are placed 0.450 m apart. What is the change in
electric potential energy of this system if a third charge of q = −2.00 µC is moved from infinitely
far away to occupy a position that is 0.450 m from each of these charges (the empty corner of an
equilateral triangle)? (i.e. How much work must we do to move a third charge of q = −2.00 µC
from infinitely far away to the empty corner?)
50
0.4
m
+3.0 µC
+3.0 µC
Question 4: Three point charges, each of +2.0 µC, are held in place to occupy the corners of an
equilateral triangle that is 0.55 m on a side. (a) Suppose that all three charges are released at the
same time, and they repel each other. What is the kinetic energy of any one charge as is approaches
a very far distance away from the other two? (b) Suppose instead that a single charge is released
while the other two remain held in place. What is the kinetic energy of the released charge as is
approaches a very far distance away from the other two?
+2.0 µC
5m
0.5
+2.0 µC
+2.0 µC