2. ELECTRIC POTENTIAL ENERGY
When a test charge is placed in an electric field, it experiences a
force.
𝑭 = 𝒒𝑬 (𝒕𝒉𝒆 𝒇𝒐𝒓𝒄𝒆 𝒊𝒔 𝒄𝒐𝒏𝒔𝒆𝒓𝒗𝒂𝒕𝒊𝒗𝒆).
If the test charge is moved in the field by some external agent,
the work done by the field is the negative of the work done by
the external agent.
3. ELECTRICAL POTENTIAL ENERGY IN A UNIFORM ELECTRICAL FIELD
The electric field between two parallel plates is an
example of a uniform electric field.
4. ELECTRICAL POTENTIAL ENERGY
The change in potential energy for a positive charge placed at
Point P if it moves to the negative plate can be expressed as:
The negative sign indicates that the
amount of PE is decreasing. Work is
being done on the charge by field.
6. UNITS
The potential difference between points A and
B, VB−VA, is thus defined to be the change in potential
energy of a charge q moved from A to B, divided by the
charge. Units of potential difference are joules per
coulomb, given the name volt (V) after Alessandro Volta.
7. UNITS
One joule is the work done to move an electric charge of
one coulomb through an electrical potential difference of
one volt, or one "coulomb-volt" (C-V).
Note: Joule is both the unit of work and energy. Even
though the unit is same for both, the two quantities are
not.
8. ELECTRICAL POTENTIAL DIFFERENCE
Electrical potential difference is defined as the work done per unit of
charge (Joules per Coulomb) while moving the charge between two
points in an electric field.
It can also be thought of as the change in PE per unit of charge
between two points in an electric field.
9. ELECTRICAL POTENTIAL DIFFERENCE
The potential difference between the positive and the negative
plates depends on the field strength and the plate separation.
Potential difference is measured in volts (1 V = 1 JC-1).
10. QUIZ - 1
Consider an electron being placed in an electrical field across
which a potential difference of 1 V is measured. Find an electric
potential energy.
11. QUIZ - 2
Suppose you have a 12.0 V motorcycle battery that can
move 5000 C of charge, and a 12.0 V car battery that can
move 60,000 C of charge. How much energy does each
deliver? (Assume that the numerical value of each charge
is accurate to three significant figures.)
12. QUIZ - 3
An electron is accelerated from rest through a potential difference 12
V. What is the change in electric potential energy of the electron?
13. QUIZ - 4
Two point charges are separated by a distance of 10 cm.
Charge on point A =+9 μC and charge on point B = -4 μC.
k = 9 x 109 Nm2C−2, 1 μC = 10−6 C.
What is the change in electric potential energy of charge on
point B if accelerated to point A
14. REAL LIFE EXAMPLE
Voltage is not the same as energy. Voltage is the energy per unit charge.
Thus a motorcycle battery and a car battery can both have the same
voltage (more precisely, the same potential difference between battery
terminals), yet one stores much more energy than the other since
ΔU = =qΔV.
The car battery can move more charge than the motorcycle battery,
although both are 12 V batteries.
15. WORK OF ELECTRICITY
When a charge accelerates, it changes speed and
experiences a change in kinetic energy, ΔK The work-kinetic
energy theorem states that changes in kinetic energy are
equal to work, W= ΔK If kinetic energy is changing, another
energy in the system must be experiencing an equal but
opposite change in order to ensure that energy is
conserved. In problems involving a moving charge, the
change in kinetic energy is offset by an equal change in
electric potential energy. This is directly proportional to the
potential difference through which the charge moves.
WE = ΔK= -ΔUE = -qΔV= -q(Vf - Vi)
16. QUIZ - 5
Find the work done on an electric charge of 2 C that is moved in
the electric field described in the picture.
17. QUIZ - ASNWER
Work is equal to a change in energy. This problem involves
equipotential lines. The energy that is changing is electric potential
energy, A This is related to the potential difference ΔUE, This is
related to the potential difference,ΔV,through which the 2-coulomb
charge moves.
W = -ΔUE = -q ΔV = -q(Vf - Vi)
W = -ΔUE =-q ΔV = -(2 C)[(-2 V) - (+4 V)]
W = +12 J
18. QUIZ - 6
Two parallel plates are charged. The separation between the
plates is 2 cm and the magnitude of the electric field between the
plates is 500 Volt/meter. What is the change in potential energy
of the proton when accelerated from the positively charged plate
to the negatively charged plate.
19. The eV
1eV is defined as the amount of energy required to move an
electron through a potential difference of 1Volt
An electron that accelerates through a potential difference
of 100V will lose 100eV of electric potential energy and gain
100eV of kinetic energy.
The eV is not a proper SI unit so we must convert to Joules
when performing calculations involving SI units.
1.0eV = 1.6x10-19J
20. ELECTRIC POTENTIAL
When an object moves in a gravitational field, it usually
experiences a change in kinetic energy and in gravitational
potential energy because there is work done on the object by
gravity. Similarly, when a charge moves in an electric field, it
generally experiences a change in kinetic energy and in
electrical potential energy because of the work done on it by
the electric field. In this chapter we will discuss electric
potentials.
21. ELECTRIC POTENTIAL ENERGY
As we said, when a charge moves in an electric field, unless
its displacement is always perpendicular to the field, the
electric force does work on the charge. If WE is the work
done by the electric force, then the change in the
charge”s electrical potential energy is defined by
ΔUE = –WE
22. CHARGE IN THE FIELD
A positive charge +q moves from position A to position B in a
uniform electric field E
What is its change in electrical potential energy?
23. CHARGE IN THE FIELD
Since the field is uniform, the electric force that the charge
feels, FE = qE, is constant. Since q is positive, FE points in the
same direction as E, and, as the figure shows, they point in
the same direction as the displacement, r. This makes the
work (W = Fd) done by the electric field equal toWE = FEr =
qEr, so the change in the electrical potential energy is
UE = –qEr
Notice that the change in potential energy is negative, which means
that potential energy has decreased; this always happens when the
field does positive work. It”s just like when you drop a rock to the
ground: Gravity does positive work, and the rock loses gravitational
potential energy.
24. QUIZ - 7
A negative charge +q moves from position A to position
B in a uniform electric field E
What is its change in electrical potential energy?
