Gravitational Potential Energy

GPE – The amount of energy a mass

possesses due to its position in a

gravitational field.

• The amount of work an object can

accomplish with respect to the

reference is equal to the potential

energy.

GPE= mgh

m

h

Mechanical system

GPE = WorkThe gravitational potential energy isequal to the amount of work need toraise the mass to a certain level.

Electrical Potential Energy

+ + + +

PE = qEd = W

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.

•The amount of work to move the charge between two locations.

• The amount of work a charge can

accomplish with respect to the

reference.

d

UniformElectricField

Conservation of Mechanical Energy

+ + + +

Electrical System

- - - -

+

d

The work accomplished by thefield in both situation is equal to the potential energy lost orthe kinetic energy gained.

1

2

PE1+KE1=PE2+KE2

If the object starts from restAnd the ends at the referenceThen

PE1=KE2

The initial potential energy of the object is equal to its finalkinetic energy.

MechanicalSystem

Specifically for a charge ina uniform electric field:qEd= ½ mv2

2

Determining the Speed of a Charge in an Electric Field

PE1=KE2 for an object that starts at rest and ends at the reference.

PE1= ½ mv2 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 mv2

q= 1.6x10-19 C E= 7200 N/C d=0.038 m me= 9.11x10-31 kg

PE= (1.6x10-19C)(7200 N/C)(.038 m) = 4.4x10-17 J

PE=KE4.4x10-17 J = ½(9.11x10-31 kg)v2

v=9.8x106 m/s

The Work-Energy Theorem

• W=ΔKE

• W=KE2-KE1

• If the charge object starts from rest, then

W=KE2

qEd= ½ mv2 for a charge in a uniform electric field

A Mechanical Analogy to Potential

h

m1

Which apple has the greatest gravitational potential energy? Why?

m2m3 PE=mgh

Suppose mass was not a factor, which location has the greatest gravitational potential energy per unit mass.

ghm

mgh

m

Work

m

PE PotentialnalGravitatio

mgh1+ ½ mv12= mgh2 + ½ mv2

2

gh1+ ½ v12= gh2 + ½ v2

2

gh = gravitational potential

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

+ + + +

- - - -

d

q1 q2q3

Which charge has the greatest electrical potential energy? Why?

PEe=qEd

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.

Edq

qEd

q

Work

q

PE PotentialElectric

V = EdV = electric potential

Uniform Field only

Electric Potential is synonymous with the term voltage.

Electric Potential is measured in a J/C renamed a Volt (V).

Electric Potential (Voltage) • 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.

The Difference Between the terms Potential Difference and Potential

+ + + +

- - - -

Potential – with respectto a defined reference

Potential Difference – Between two locations ΔV V

Potential Difference is denoted as ΔV.reference

Potential/Potential Difference/Voltage:• 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)

Electric Potential Energy and Voltage

• V=Ed (Uniform Electric Field)

• W=PE=qEd (Uniform Electric Field)

• W= PE = qV (general)

Water Analogy of PotentialThe 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 potentialenergy which will be converted tokinetic energy due to workaccomplished by the stream of water.

Potential Energy and Voltage (Potential) Comparison

Positive Charge

Negative Charge

PE: low PE: medium PE: highThe voltage (potential) is the same in all three situations.

PE: lowVoltage: low PE: medium

Voltage: medium

PE: highVoltage: high

PE: highVoltage: high

PE: mediumVoltage: med

PE: lowVoltage: low

Potential/Potential Difference/Voltage Change

• 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

r

QkV

rB

rA

Q

W=qV=ΔEnergy

q

(with respect to infinity)

AB r

1

r

1kQV

AB r

1

r

1kQqW

The electric field is not uniform for point charges.

Q - the charge causing the field q – the charge in the field

ΔV = potential difference (voltage)

V = potential (voltage)

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 1.6x10-19J. Since this is an extremely small amount of work an new unit was devised.

1eV=1.6x10-19 J

The Work on a Small Amount of Charge

1eV = 1 electron-Volt (A unit of work or energy)

Charge Electric Potential Energy

W=qV =ΔE (general)W=qEd=ΔE (uniform electric field)

Charge Electrical Potential (Voltage)V=W/q=PE/q (general)V=Ed (uniform electric field)

(point charge)

Potential Difference (Voltage) and Potential Energy Equations

(point charge)

AB r

1

r

1kQV

AB r

1

r

1kQqW

End

Positive Charge

Negative Charge

PE: highVoltage: highΔKE: +ΔPE: -

PE: lowVoltage: lowΔKE: +ΔPE: -

PE: lowVoltage: lowΔKE: +ΔPE: -

PE: lowVoltage: lowΔKE: +ΔPE: -

PE: lowVoltage: lowΔKE: +ΔPE: -

PE: lowVoltage: lowΔKE: +ΔPE: -