Mechanical system m
GPE – The amount of energy a mass possesses due to its position in a gravitational field. h
• The amount of work an object can accomplish with respect to the reference is equal to the potential energy.
GPE= mgh
GPE = Work
The gravitational potential energy is equal to the amount of work need to raise the mass to a certain level.

-
Electrical System
+ + + +
+
Electrical Potential Energy - the amount of electrical energy a charge possesses due to its position in an electrical field.
.
•The charge’s stored energy.
d
•The amount of work to move the charge between two locations.
-
• The amount of work a charge can accomplish with respect to the reference.
PE = qEd = W
Uniform
Electric
Field

Mechanical
System
Electrical System
+ + + +
The work accomplished by the field in both situation is equal to the potential energy lost or the kinetic energy gained.
1
+
PE
1
+KE
1
=PE
2
+KE
2 d If the object starts from rest
And the ends at the reference
Then
-
2
PE
1
=KE
2
The initial potential energy of the object is equal to its final kinetic energy.
Specifically for a charge in a uniform electric field: qEd= ½ mv
2
2

Determining the Speed of a Charge in an Electric Field
PE
1
=KE
2 for an object that starts at rest and ends at the reference.
PE
1
= ½ mv 2 solve for v to obtain the speed of a charge.
An electron starts at the negative terminal of parallel plates with an electric field
Intensity of 7200 N/C that are separated by 3.8 cm. What is the speed obtained by the electron at the positive plate?
PE = qEd
(Uniform Electric Field)
KE = ½ mv 2 q= 1.6x10
-19 C E= 7200 N/C d=0.038 m m e
= 9.11x10
-31 kg
PE= (1.6x10
-19 C)(7200 N/C)(.038 m) = 4.4x10
-17 J
PE=KE
4.4x10
-17 J = ½(9.11x10
-31 kg)v 2 v=9.8x10
6 m/s

2
1
2
2

h m
1
Which apple has the greatest gravitational potential energy?
Why?
m
2 m
3 PE=mgh
Suppose mass was not a factor, which location has the greatest gravitational potential energy per unit mass.
Gravitatio nal Potential

PE m

Work
 mgh m m
 gh mgh
1
+ ½ mv
1
2 = mgh
2
+ ½ mv
2
2 gh
1
+ ½ v
1
2 = gh
2
+ ½ v
2
2 gh = gravitational potential

• The gravitational potential energy per unit mass.
• The work per unit mass to raise a mass to a specific height from a reference
• The capability of the gravitational field of giving a mass gravitational potential energy at a specific height.
• A quantity representing the amount of gravitational potential energy a mass would have if located at the specific position.
• A quantity representing the amount of gravitational potential energy with respect to a defined reference without consideration of the mass.

Electric Potential/Electric Potential Difference/Voltage
+ + + + Which charge has the greatest electrical potential energy?
Why?
PE e
=qEd q
1 q
2 q
3 d
Suppose the charge was not considered, which location has the greatest energy per unit charge.
-
The size of the charge represents the relative quantity of charge.
Electric Potential

PE q

Work q
 qEd q

Ed
V = Ed
Uniform Field only
V = electric potential
Electric Potential is synonymous with the term voltage .
Electric Potential is measured in a J/C renamed a
Volt (V).

• The electrical potential energy per unit charge.
• The work per unit charge to move the charge a distance from a reference.
• The electric field’s relative capacity of giving a charge electrical potential energy at a specific location in an electric field.
• A quantity representing the relative amount of electrical potential energy a charge would have if located at the specific position.
• Electric Pressure exerted by the electric field.
• Electric Potential (Voltage) is a scalar quantity.
• Potential is a property of the electric field itself.

+ + + +
Potential
Difference –
Between two locations ΔV V
Potential – with respect to a defined reference
-
Potential Difference is denoted as ΔV.
reference

• The terms are used interchangeably are denoted with the letter V.
• Potential is with respect to a defined reference.
• Measured with the unit Joule/Coulomb which is renamed a Volt (V)
• Scalar quantity
• A potential difference between locations is needed for charge to move.
• Positive charges always move in the direction of decreasing potential and negative charges toward increasing potential.
• V=Ed
(uniform electric field)

(Uniform Electric Field)
(Uniform Electric Field)
(general)

The stream of water has potential
Itself at a given location regardless of a mass being present in the stream of water.
A mass now placed in the field of water would now posses potential energy which will be converted to kinetic energy due to work accomplished by the stream of water.

Potential Energy and Voltage (Potential) Comparison
PE: low PE: medium
PE: high
The voltage (potential) is the same in all three situations.
PE: low
Voltage: low
PE: high
Voltage: high
PE: medium
Voltage: medium
PE: medium
Voltage: med
PE: low
Voltage: low
PE: high
Voltage: high
Positive Charge
Negative Charge

• Because Potential/Potential Difference/voltage only consider the electric field, the convention is to consider a decreasing potential in the direction of the electric field .
+
The potential decreases away from a positive charge
-
The potential increases away from a negative charge

Potential and Potential Energy of a Point Charge
The electric field is not uniform for point charges.
r
B
V
 k
Q
(with respect to infinity) r
V = potential (voltage) q

V
 kQ


1 r
B

1 r
A

 r
A
Q ΔV = potential difference (voltage)
W=qV= ΔEnergy
W
 kQq


1 r
B

1 r
A


Q - the charge causing the field q – the charge in the field

W=qV = ΔE
W=(1.6x10
-19 C)(1.0 V) =1.6 x 10 -19 J
The amount of work to move an electron or proton through a potential of a 1.0 V is 1.6x10
-19 J. Since this is an extremely small amount of work an new unit was devised.
-19
1eV = 1 electron-Volt
(A unit of work or energy)

Potential Difference (Voltage) and Potential Energy Equations
Charge Electrical Potential (Voltage)
V=W/q=PE/q (general)
V=Ed (uniform electric field)

V
 kQ


1 r
B

1 r
A

 (point charge)
Charge Electric Potential Energy
W=qV = ΔE (general)
W=qEd= ΔE
(uniform electric field)
W
 kQq


1 r
B

1 r
A

 (point charge)

End

PE: high
Voltage: high
ΔKE: +
ΔPE: -
PE: low
Voltage: low
ΔKE: +
ΔPE: -
PE: low
Voltage: low
ΔKE: +
ΔPE: -
Positive Charge
Negative Charge
PE: low
Voltage: low
ΔKE: +
ΔPE: -
PE: low
Voltage: low
ΔKE: +
ΔPE: -
PE: low
Voltage: low
ΔKE: +
ΔPE: -