TUTORIAL 4
CHARGE
2/7/17
Lecture Instructor: Dr. David Smith
Coulomb’s Law
¨
2/7/17
Coulomb’s law states that the electric force between two point
charges acts along the line connecting the two point charges. (A
point charge is a charged object that is sufficiently small that
the charge can be treated as it it were all located at a single
point.) The magnitude of the force on either of the charges is
proportional to the product of the charges and is inversely
proportional to the square of the distance between the
charges.
Discussion Questions
¨
Two positive point charges +q and +Q (with 𝑄 > 𝑞 )
are held in place a distance s apart.
1. Indicate the direction of the electric force exerted on the
+q charge by the +Q charge.
2. Is the magnitude of the force on the +q charge by the
+Q charge greater than, less than, or equal to the
magnitude of the force on the +Q charge by the +q
charge? Explain.
3. By what factor would the magnitude of the electric force
on the +q charge change if the charges were instead
separated by a distance 2s?
2/7/17
Quiz: 1
¨
Which of the choices below best matches your
answers to the previous questions.
A. Upward, less than, decreases by a factor of 4
B. Upward, equal to, decreases by a factor of 2
C. Downward, less than, decreases by a factor of 4
D. Upward, equal to, decreases by a factor of 4
E. Downward, greater than, decreases by a factor of 2
F. Other
2/7/17
2/7/17
Quiz: 2
¨
¨
¨
Two more +Q charges are held in place the same distance
s away from the +q charge as shown. Consider the
following student dialogue concerning the net force on the
+q charge.
Student 1: “The net electric force on the +q charge is now
three times as large as before, since there are now three
positive charges exerting forces on it.”
Student 2: “I don’t think so. The force from the +Q charge on
the left will cancel the force from the +Q charge on the right.
The net electric force will the same as part A.”
1. Do you agree with either student?
¨
A: Student 1
B: Student 2
C: Neither student
Quiz: 3
¨
2/7/17
Rank the four cases below according to the magnitude of the net electric force on
the +q charge. Explain your reasoning to your neighbor.
Discussion Question
¨
¨
¨
¨
¨
¨
2/7/17
In case A at right, a point charge +q is a
distance s from the center of a small ball
with charge +Q.
In case B the +q charge is a distance s
from the center of an acrylic rod with a
total charge +Q.
Consider the following student dialogue.
Student 1: “The charged rod and the charged ball have the same charge, +Q, and are the same
distance from the point charge, +q. So the force on +q will be the same in both cases.”
Student 2: “No, in case B there are charges spread all over the rod. The charge directly below the
point charge will exert the same force on the +q as the ball in case A. The rest of the charge on
the rod will make the force in case B bigger.”
Neither student is correct. Discuss with your neighbors the errors made by each student. Write
a correct description of how the forces compare in each case.
Discussion Question
¨
¨
2/7/17
Two identical metal balls are suspended by insulating threads. Both balls have the
same net charge. In this problem, do not assume the balls are point charges.
Draw a separate free-body diagram for each ball.
Quiz: 4
¨
¨
2/7/17
Suppose the charge on the second ball is reduced slightly, so that is is less than
that on the first ball.
Will the angle that ball 1 makes with the vertical be greater than, less than, or
equal to the angle that ball 2 makes with the vertical. Sketch your answer below.
2/7/17
Quiz: 5
Which of the illustrations below best represents what would happen if the net
charge on ball 2 is reduced to zero.
¨
A
B
C
D
Quiz: 6 & 7
¨
¨
¨
¨
2/7/17
A thin semicircular rod has a total charge +Q uniformly
distributed along it. A negative point charge –Q is
placed as shown. A test charge +q is placed at point C.
(Point C is equidistant from –Q and from all points on
the rod.)
Let 𝐹% and 𝐹& represent the force on the test charge
due to the point charge and the rod respectively.
Is the magnitude of 𝐹% greater than, less than, or equal to the magnitude of 𝐹& ?
Explain your reasoning to your neighbor.
Is the magnitude of the net force on the +q greater than, less than, or equal to the
magnitude of 𝐹& ? Explain your reasoning to your neighbor.
Quiz: 8
¨
¨
A second negative point charge –Q is placed as
shown.
Is the magnitude of the net electric force on the
+q greater than, less than, or equal to the
magnitude of the net electric force on +q in
question 7 on the previous slide? Explain your
reasoning to your neighbor.
2/7/17