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Electric Potential Energy
And
Electric Potential
• Gravitational forces
store mechanical work
in the form of potential
energy ( PE)
• Mechanical work that is
stored as electric
energy is called electric
potential energy
When is mechanical work done in an
electrical system?
When is mechanical work done in an
electrical system?
Opposite charges
Like charges
Separating two charges that
attract each other requires
mechanical work.
• Moving two charges that
repel each other closer
together requires
mechanical work
Work is stored in the electric
field as electric potential
energy
• This work is stored in the
electric fields as electric
potential energy.
Calculating work done in an Electric Field
•  In an Uniform electric field.
• +q is placed in the field and
experiences a downward
electrical force ( F = qE)
• When charged is moved upwards
( distance d) -- electric force and
displacement are in opposite
direction
• Work done by electric force is
negative and equal in magnitude
to the force times distance.
• W=-qEd
Equation for Work and
potential energy
• Δ PE = -W Gives a direct
connection between the work
done to move charges in an
electric field and the system’s
change in electric potential
energy:
• Δ PE = -W
• Δ PE = q E d
Electric potential energy
increases in this case. Like raising
the ball against the force of
gravity.
Voltage is the electric potential energy
per charge
• Electric Potential, V
• Change in electric potential = Change in electric potential energy
•
charge
• Δ V = Δ PE / q
• SI unit: joules/ coulomb = Volt ( V )
• Volt is named after Alessandro Volta who invented
the battery.
Units of Voltage
• The volt has the units of
energy ( J ) per charge (
C)
• 1 V = 1 J/C
1 joule of energy is equal
to 1 coulomb times 1 volt
1J=(1C)(1V)
• A 1.5 V battery does 1.5
j work for every
coulomb of charge
• ( 1 C ) ( 1.5 V ) = 1.5 J
What is the change in electric
potential energy ?
• Find the change in electric potential energy, Δ
PE , as a charge of 2.20x10-6C moves from
point A to point B, given that the change in
electric potential between these points is
ΔV=24.0V
Find the change in electric potential energy, Δ PE , as a charge of 2.20x10-6C
moves from point A to point B, given that the change in electric potential
between these points is ΔV=24.0V
• Using
• ΔPE = q Δ V
2.20x10-6 C) ( 24.0 V)
• = 5.28x10-5 J
• =(
Widely separated unlike charges produce high
voltage because they store a lot of energy .
Like charges close together produce high
voltage because they store a lot of energy.
Electric potential is related to the
electric field
• The magnitude W = q E d
• Therefore the change in electric potential is
• Δ V = Δ PE / q = -W/q = - (q Ed) q = -Ed
Connection between Electric field and
the Electric Potential
• Electric field = - change in electric potential
distance
E=ΔV/d
SI units: volts / meter (V/m)
• Charge q moves in the
direction of the electric
field,( E ) a distance (d).
• Electric potential (V)
decreases by the amount
• Δ V = -Ed
• Electric field depends on
the rate of change of the
electric potential with
position
Gravitational analogy for electric
potential (V) and electric field (E)
Uniform electric field
The electric potential (V) decrease as q moves in the direction
of the electric field . In this case the electric field is constant,
electric potential decreases uniformly with distance.
Relative to the electric field in what direction does the electric
potential decrees?
• The electric potential
decreases in the
direction of the electric
field.
• Electric potential does’t
change at all in the
direction perpendicular
to the electric field.

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