Electric Potential Energy and
Electric Potential
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Learning Objectives
By the end of this lesson, you will be able to:
Describe electric potential, potential energy, and potential difference, and
explain their relationships to electric field and work.
Express the unit of electric potential in volts and interpret the meaning of
one electron volt (eV).
Distinguish between conservative and non-conservative forces in
electrostatics.
Relate electric potential energy to charge movements and energy
conservation.
Apply the concepts of electric potential and potential difference to
practical situations and problem solving.
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The Electric Potential
Moving an electric charge through space where
electric fields are present can require work, since
forces associated with the fields act on the charge.
This work can be described as a change in potential
energy. We introduce the new concept of “electric
potential” to describe the amount of work needed to
move a charge through a region with electric fields.
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A difference in electrical potential between the upper
atmosphere and the ground can cause electrical discharge
(motion of charge).
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Two parallel metal plates containing equal but
opposite-sign charges produce a uniform electric
field in the region between the plates.
“CAPACITOR”
(This is a convenient device that allows us to talk about a
region where the electric field does not change. This
makes the calculations much easier.)
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An external force F, equal in magnitude to the electrostatic
force qE, is used to move the charge q a distance d in a
uniform field.
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The increase in potential energy when a charge q is
moved against the electrostatic force is analogous to
what happens when a mass m is lifted against the
gravitational force.
We call this the electrostatic potential energy (instead of the gravitational
potential energy).
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The change in electric potential is equal to the change in
electrostatic potential energy per unit of positive test charge:
PE
V =
q
The electrical Potential V at a given point is the electric potential
energy PE of a small test charge qo situated at that point
divided by the charge it self. This is the definition of electrical
potential.
It is measured in volts (V).
Electrical potential is the “push” a charged particle would feel
at a point in an electric field, measured as energy per unit
charge.
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Potential Difference (V)
• The potential difference between two points in an electric
field is the amount of work done per unit of charge as a
charge is moved between two points.
• Mathematically:
• Potential Difference = Work Done
Charge
W
V=
q
Rearrange to
W = qV
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• The volt
• One volt is the potential difference
between two points in an electric field
when one joule of work is done in moving a
charge of 1 C between these points.
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The Electron Volt, a Unit of Energy
A Joule is too large when dealing with electrons or atoms, so electron
volts are used. One electron volt (eV) is the energy gained by an
electron moving through a potential difference of one volt.
If a 1-volt potential difference accelerates an electron, the electron
acquires 1 electron-volt worth of kinetic energy.
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The Electron Volt
• The electron volt (eV) is defined as the energy
that an electron gains when accelerated through a
potential difference of 1 V
– Electrons in normal atoms have energies of 10’s of eV
– Excited electrons have energies of 1000’s of eV
– High energy gamma rays have energies of millions of
eV
• 1 eV = 1.6 x 10-19 J
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Electrostatic Potential Energy and
Potential Difference
The image shows the electric field and potential
between two parallel plates.
▪ The electric field (E) is uniform and points
from the positively charged plate to the
negatively charged plate.
▪ A positive charge moves from a region of
high potential and high potential energy (PE)
towards a region of low potential and low
potential energy.
▪ The work done by the electric field on a
positive charge as it moves from point 'a' to
point 'b' is positive.
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Electric Potential and Potential
Difference
• Place a test charge, q0, into an E-field. The charge
will experience
 a force:

F = q0 E
• Pretend an external agent does work to move the
charge through the E-field.
The work done by the external agent equals at least
the negative of the work done by the E-field.
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• This force is a conservative force.
Some Typical Potential Differences
(Voltages)
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Electric Potential Energy
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Work and Potential Energy
There is a uniform field between the two
plates
If the charge moves along the direction of the field, the field does
positive work (it helps the motion).
If it moves opposite to the field, the field does negative work (it
resists the motion).
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When a force acts over a displacement, work is done by the field.
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Work and Potential Energy
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Work and Potential Energy
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When the electric field does work on
a charge, the electric potential
energy (PE) of that charge changes.
If the field does positive work (the
charge moves in the direction of the
field), the charge loses potential
energy.
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Potential Difference
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Potential Difference, cont.
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Energy and Charge Movements
➢ Positive charge gains electric potential energy when it is
moved against the direction of the electric field.
➢ If the charge is released, the electric field exerts a force on
it, causing it to accelerate and gain kinetic energy.
➢ As the charge gains kinetic energy, it loses an equal amount
of electric potential energy — energy is conserved.
➢ A negative charge, on the other hand, loses electric
potential energy when it moves against the electric field.
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• When the electric field is
directed downward, point B
is at a lower potential than
point A
• A positive test charge that
moves from A to B loses
electric potential energy
• It will gain the same amount
of kinetic energy as it loses in
potential energy
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Energy and Charge Movements,
cont…..
Summary of Positive Charge
Movements and Energy
• When a positive charge is placed in an electric
field
– It moves in the direction of the field
– It moves from a point of higher potential to a
point of lower potential
– Its electrical potential energy decreases
– Its kinetic energy increases
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Summary of Negative Charge
Movements and Energy
• When a negative charge is placed in an electric field
– It moves opposite to the direction of the field
– It moves from a point of lower potential to a point
of higher potential
– Its electrical potential energy increases
– Its kinetic energy increases
– Work has to be done on the charge for it to move
from point A to point B
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Potential Difference in a
Uniform E-Field
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Potential Difference in a
Uniform E-Field
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Potential Difference in a
Uniform E-Field
Electric fields accelerate charges… that’s what
they do.
What we’re saying here is that as the E-field
accelerates a positive charge, the charge-field
system picks up kinetic energy.
Why? Because in an isolated system without
friction, mechanical energy must always be
conserved.
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At the same time, the charge-field system loses an
equal amount of potential energy.
Electric Potential of a Point
Charge
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Electric Field and Electric
Potential Depend on Distance
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Electrical Potential Energy of Two
Charges
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• V1 is the electric potential
due to q1 at some point P
• The work required to bring q2
from infinity to P without
acceleration is q2V1
• This work is equal to the
potential energy of the two
particle system
q1q 2
PE = q 2 V1 = k e
r
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Notes About Electric Potential
Energy of Two Charges
• If the charges have the same sign, PE is positive
– Positive work must be done to force the two
charges near one another
– The like charges would repel
• If the charges have opposite signs, PE is negative
– The force would be attractive
– Work must be done to hold back the unlike
charges from accelerating as they are brought
close together
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Electrostatic Potential Energy and
Potential Difference
Electric potential (or Potential Difference) is
defined as potential energy per unit charge:
Electric potential is not Potential Energy.
Unit of electric potential: the volt (V).
1 V = 1 J/C.
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Electric Potential
The potential at a given point
The electric potential at a point shows
how much energy a positive charge
would have at that point.
It has units of
Energy
joules
Volts =
=
charge coulomb
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Electric Potential
General Points for either positive or negative charges
The Potential increases if you move in the
direction opposite to the electric field
and
The Potential decreases if you move in the
same direction as the electric field
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Equipotential Surfaces
• An equipotential surface is a surface on which
all points are at the same potential
– No work is required to move a charge at a
constant speed on an equipotential surface
– The electric field at every point on an
equipotential surface is perpendicular to the
surface
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Equipotential Lines
An equipotential (represented by the
green dashed lines) is a line or
surface over which the potential is
constant.
Electric field lines are perpendicular
to equipotentials.
The surface of a conductor is an
equipotential.
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• The equipotentials for a
point charge are a family of
spheres centered on the
point charge
• The field lines are
perpendicular to the electric
potential at all points
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Equipotentials and Electric
Fields Lines – Positive Charge
Equipotential Lines
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Application – Electrostatic
Precipitator
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• It is used to remove particulate
matter from combustion gases
• Reduces air pollution
• Can eliminate approximately
90% by mass of the ash and
dust from smoke
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Application – Electrostatic Air
Cleaner
• Used in homes to relieve the discomfort of
allergy sufferers
• It uses many of the same principles as the
electrostatic precipitator
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Application – Xerographic
Copiers
• The process of xerography is used for making
photocopies
• Uses photoconductive materials
– A photoconductive material is a poor conductor of
electricity in the dark but becomes a good electric
conductor when exposed to light
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The Xerographic Process
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Application – Laser Printer
▪ A laser printer operates similarly to the xerographic
(photocopying) process. Steps such as charging, developing, and
transferring are the same.
▪ The main difference lies in how the image is created on the
selenium-coated drum.
▪ A rotating mirror directs a laser beam across the drum, forming
the image by creating positive charge patterns that represent
the letters or images to be printed.
▪ Toner particles then stick to these charged areas, and the
remaining steps proceed just like in the xerographic process.
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Potential Differences in
Biological Systems
The Membrane Potential of Neurons
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Potential Differences in
Biological Systems
▪ The axons of nerve cells (neurons) are long extensions that
transmit electrical signals.
▪ In the resting state, the fluid inside a neuron is about –85 mV
relative to the fluid outside. This difference comes from unequal
concentrations of positive and negative ions on either side of the
membrane.
▪ When a nerve impulse occurs, the outer membrane becomes
temporarily permeable to Na⁺ ions (sodium ions) for about 0.2
milliseconds.
▪ As Na⁺ rushes into the cell, the inside fluid’s charge reverses:
from about –85 mV to about +60 mV.
▪ To restore the resting state, K⁺ (potassium) diffuses out of the cell
and Na⁺ ions are pumped out via active transport (Na⁺/K⁺
pump).Maintaining the resting potential and active transport can
consume up to 20% of the body’s energy in neurons.
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Potential Differences in Medicine
• Polarity changes across membranes of muscle cells
– Muscle cells have a layer of – ions on the inside of the
membrane and + ions on the outside
– Just before each heartbeat, + ions are pumped into the cells,
neutralizing the potential difference (depolarization)
– Cells become polarized again when the heart relaxes
• Electrocardiogram (EKG)
– Measures potential difference between points on chest as a
function of time
– Polarization and depolarization of cells in heart causes potential
differences that are measured by electrodes
• Electroencephalogram (EEG) and Electroretinogram (ERG)
– Measures potential differences caused by electrical activity in
the brain (EEG) and retina (ERG)
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Lab Safety
Chemistry & Physics
Your safety is our top priority.
Dress for Success and Safety
Personal Protective Equipment (PPE)
•EYES: Safety Goggles - ON AT ALL TIMES.
•BODY: Lab Coat - Fastened and intact.
•HANDS: Appropriate Gloves - Nitrile for chemicals, heat-resistant for
physics.
•FEET: Closed-Toe Shoes - No sandals, no exceptions.
•CLOTHING: Fitted, non-flammable. Tie back long hair and secure
loose sleeves/bags.
General Conduct
Lab Conduct: Zero Tolerance
•NO food, drink, gum, or cosmetics.
•NO unauthorized experiments.
•NO horseplay, running, or distractions.
•YES to staying focused and at your assigned
station.
Before You Start
Be Prepared: Before the Lab
1.READ the entire procedure beforehand.
2.KNOW the hazards of the chemicals and equipment you will use.
3.LOCATE all safety equipment:
1. Eye Wash & Safety Shower
2. Fire Extinguisher & Blanket
3. First Aid Kit & Spill Kits
4. Fume Hoods & Exits
Chemistry-Specific Safety
Handling Chemicals Safely
•Use the FUME HOOD for volatile/toxic substances.
•WAFT to smell, never inhale directly.
•ADD ACID TO WATER, slowly.
•Never return unused chemicals to stock bottles.
•Label all containers clearly.
Physics-Specific Safety
Handling Physics Equipment Safely
•Inspect for DAMAGED CORDS or equipment before use.
•Be cautious with HEAT SOURCES and ROTATING
MACHINERY.
•Keep areas clear when using PROJECTILES.
•NEVER look directly at a laser beam.
Clean-Up & Disposal
The Lab is Not Done Until it's Clean
•DISPOSE of waste in the correct, labeled containers.
•CLEAN all glassware and equipment.
•RETURN items to their proper storage.
•WIPE DOWN your bench.
•TURN OFF gas & water.
•WASH YOUR HANDS thoroughly before leaving.
In Case of Emergency
Emergency Procedures
•SPILLS: Alert the instructor immediately. Do not clean unless trained.
•FIRE: Alert everyone. Use an extinguisher only on small fires if trained.
Otherwise, EVACUATE.
•INJURY: Report ALL injuries, no matter how small, to the instructor
immediately.
•EYE EXPOSURE: Flush at the eye wash station for 15 MINUTES.
Final Rule
The Golden Rule of the Lab
If you are unsure about ANY procedure, substance, or piece of
equipment...
STOP and ASK YOUR INSTRUCTOR.
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