2. 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 = Work The gravitational potential energy is equal to the amount of work need to raise the mass to a certain level.

3. 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 Uniform Electric Field

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

5. 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 CE= 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

6. The Work-Energy Theorem W=ΔKE W=KE 2 -KE 1 If the charge object starts from rest, then W=KE 2 qEd= ½ mv 2 for a charge in a uniform electric field

7. A Mechanical Analogy to Potential h m1m1 Which apple has the greatest gravitational potential energy? Why? m2m2 m3m3 PE=mgh Suppose mass was not a factor, which location has the greatest gravitational potential energy per unit mass. 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

8. 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.

9. Electric Potential/Electric Potential Difference/Voltage + + - - d q1q1 q2q2 q3q3 Which charge has the greatest electrical potential energy? Why? PE e =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. V = Ed V = 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).

10. 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.

11. The Difference Between the terms Potential Difference and Potential + + - - Potential – with respect to a defined reference Potential Difference – Between two locations ΔVΔV V Potential Difference is denoted as ΔV. reference

12. 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)

13. Electric Potential Energy and Voltage V=Ed (Uniform Electric Field) W=PE=qEd (Uniform Electric Field) W= PE = qV (general)

14. Water Analogy of Potential 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.

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

16. 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

17. Potential and Potential Energy of a Point Charge rBrB rArA Q W=qV=ΔEnergy q (with respect to infinity) The electric field is not uniform for point charges. Q - the charge causing the fieldq – the charge in the field ΔV = potential difference (voltage) V = potential (voltage)

18. 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. 1eV=1.6x10 -19 J The Work on a Small Amount of Charge 1eV = 1 electron-Volt (A unit of work or energy)

19. 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)

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