Download Collaborative Problem 1

Name:
PHY 227 Workshop 1
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PART I: COULOMB’S LAW
Coulomb’s law describes the interaction between point charges. Each charge exerts a force on the other
that is proportional to the product of the charges and is inversely proportional to the square of the distance
between the charges.
A. Two positive point charges +q and +Q (with |Q| > |q|) are held in place a distance s apart.
1. Is the force on the +q charge by the +Q charge greater than, less than, or equal to
the force on the +Q charge by the +q charge?
2. 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?
B. Two more +Q charges are held in place the same distance s away from the +q
charge as shown. Consider the following dialogue concerning the net force on
the +q charge:
Statement 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.”
Statement 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 be the same as in part A.”
1. With which statement, if either, do you agree? Note, agreeing with both statements 1 and 2 or neither
of them is also a valid choice. Explain in words your viewpoint clearly. (Hint: Identify all the forces
on +q, draw the free-body diagram, and try to break down the forces on +q into their respective x- and
y-components.)
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PHY 227 Workshop 1
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2. What is the direction of the net electric force on the +q charge? In answering this, draw the freebody diagram, identifying all the forces on +q, and break down the forces on +q into their respective xand y-components.
3. Suppose that the two outer +Q charges are replaced with –3Q charges as
shown in the illustration to the right. (Assume that θ is between 0º and 90º
degrees.) Is it possible that the net electric force on +q is zero? Explain in words.
(Hint: Proceed exactly as you did in question 2. Identify all the forces on +q,
draw the free-body diagram, and break down the forces on +q into their
respective x- and y-components.)
-3Q
-3Q
4. How does the net force acting on +q for θ = 0º compare to the net force for θ = 90º? Describe in
words.
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Name:
PHY 227 Workshop 1
Partner name:
PART II: THE FIELD CONCEPT
The field model that you learned while doing the pre-recitation problem is useful for electrical
interactions as well. When two point charges interact, we can designate one of them as the source charge.
The source charge creates an electrical influence – or electric field – in the surrounding region of space.
The other electric charge – referred to as the probe charge or test charge – responds to this field by
experiencing a force. The field concept is especially useful in the context of charge because we usually
sum up the effects of many charges (as we did in PART I, question B+C) in a charge distribution when we
consider the electric field in a region of space. The electric field can be thought of as a measure of the
“electrical influence” at a particular location.
A. Inventing an Electrical Influence Index
Your task now is to invent an Electrical Influence Index. Imagine that a charged particle (called the “probe
particle”) is placed at some location in space, and experiences an electrical force from a collection of other
charges (the “source charges”) that are arranged in some unknown way in the general vicinity. Come up
with one number to stand for the magnitude of the electrical influence of the source charges at each
of the three locations. (Hint: Recall the pre-recitation problem.)
Here are some rules we want you to follow:
• Make sure the index describes the location, not the probe charge.
• Different locations may have different index values, or they may be the same.
• Different measurements for the same location must give the same index value!
A 4-unit probe charge
experiences 120 N of force
1. In words, provide an interpretation of the electrical influence index, in everyday terms. What does
its value tell you about the location?
2. What if a 4-unit probe charge was placed at Location 2. How large of a force would this probe
charge experience?
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