Download Reading Guide for Ch. 19, Electric Potential Energy and Electric

Brock University
Physics 1P22/1P92
Winter 2015
Dr. D’Agostino
Reading Guide for Ch. 19, Electric Potential Energy and Electric Potential
The concept of electric potential provides an alternative way of describing electric fields. At least
that is my perspective for the purposes of this course. An electrician might have a quite different
perspective, and might think in terms of potential and potential difference (what electricians call
“voltage” and “voltage drop,” respectively).
It’s a matter of perspective, because one can obtain equivalent understandings of electrical phenomena by thinking in terms of electric potential or electric field. We just finished studying mechanics
in PHYS 1P21/1P91, and so it’s perhaps natural for us to focus on the electric field: According
to Newton’s second law of motion, a particle accelerates if there is a non-zero net force acting on
it, and if the force is an electric force than we say that the electric force is caused by an electric
field.
Even if we adopt this perspective that the electric field is primary, it is helpful to understand
alternative perspectives, and you will find in other courses that electric potential is often treated
as primary (for example, in understanding nerve impulses or electrical activity in biological cells).
Electric potential often helps us understand electrical phenomena, as we shall see in this course in
the following chapter, where we discuss electric circuits.
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Potential Energy
You might like to review the concept of gravitational potential energy, as studied in first-semester
mechanics. There are all kinds of potential energy, such as elastic potential energy, chemical
potential energy, nuclear potential energy, and so on, but to understand electric potential energy
it’s probably best to make an analogy with gravitational potential energy.
The point of this section and the following one is to make the analogy between gravitational
potential energy and electric potential energy. This section reviews gravitational potential energy,
and the next one introduces electrical potential energy.
ˆ What is gravitational potential energy? What is the formula for gravitational potential energy?
ˆ Suppose you raise an object at a constant speed. How does the work you do against the
gravitational force on the object relate to the change in the gravitational potential energy of
the object?
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Electric Potential
ˆ What is electric potential energy? What is the unit for electric potential energy?
ˆ What is electric potential? What is the unit for electric potential?
ˆ What is the formula that relates electric potential energy to electric potential?
ˆ How do positively charged particles move when they are released from rest in regions of space
where the electric potential is not constant?
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ˆ How do negatively charged particles move when they are released from rest in regions of space
where the electric potential is not constant?
ˆ What is an electron-volt? How does it relate to the corresponding SI unit?
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Electric Potential for a Point Charge
The electric potential for a system of charges might be extremely complicated, in the same way
that the electric field for a system of charges might be extremely complicated. As usual, we like
to start with simple systems and understand them first, and then move on to tackle more complex
systems. The potential of a point charge is a relatively simple starting point.
ˆ What is the formula for the electric potential for a point charge?
ˆ A certain convention is used for the “zero level” of potential in the formula for the potential
of a point charge. What is this convention?
ˆ Is there a superposition principle for electric potential? Explain.
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Equipotential Surfaces and their Relation to Electric Fields
Just as there are diagrams of a certain style that help us visualize electric fields (that is, collections
of arrows or collections of electric field lines), a collection of equipotential surfaces also helps us to
visualize an electric field.
There is a nice analogy with topographical maps, and we’ll discuss this analogy in class, even
though it’s not discussed in the textbook. An equipotential surface is a lot like a contour line on a
topographical map.
Electric field lines satisfy certain properties, which tell us important things about electric fields.
Similarly, equipotential surfaces satisfy various properties, which tell us similarly important things
about electric fields.
ˆ Describe the equipotential surfaces for a positive point charge.
ˆ Describe the equipotential surfaces for a negative point charge.
ˆ Describe the equipotential surfaces for an electric dipole.
ˆ Describe the equipotential surfaces for a constant electric field, such as might be found inside
a parallel-plate capacitor.
ˆ Describe the general properties of equipotential surfaces. It may help you to think in terms
of topographical maps.
ˆ How is the electric field related to the gradient of the electric potential?
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Capacitors and Dielectrics
Capacitors store electric potential energy, and so they are important in many electrical and electronic devices. Parallel-plate capacitors provide a relatively simple example of a system in which
the electric field is (nearly) constant.
ˆ What is the capacitance of a capacitor? What is the SI unit for capacitance?
ˆ What is the relation between the magnitude of the charge on one plate of a parallel-plate
capacitor, the capacitance of the capacitor, and the potential difference of the plates?
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ˆ What is a dielectric?
ˆ What is the effect on a capacitor if a dielectric material is placed between its plates?
ˆ What is a formula for the capacitance of a parallel-plate capacitor in terms of its dimensions?
ˆ How much energy can be stored in a capacitor’s electric field? What are the relevant formulas?
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Biomedical Applications of Electric Potential Differences
OMIT this section. We won’t discuss it in lectures or tutorials, and it won’t appear on tests and
exams.
Of course, some of you will love reading and learning this material, just for the joy of it, maybe on
a rainy day in the summer.
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