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1 W03D2 Work, Potential Energy and Electric Potential Today’s Reading Assignment: Course Notes: Sections

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Announcements W03D3 Reading Assignment Course Notes: Sections Exam One Thursday Feb 28 7:30-9:30 pm Room Assignments (See Stellar webpage announcements) 2

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3 Outline Electrical Work Electric Potential Energy Electric Potential Difference Calculating Electric Potential Difference

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4 Electrical Work Work done by electrical force moving object 1 from A to B: Electrical force on object 1 due to interaction between charged objects 1 and 2: PATH INTEGRAL

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5 Concept Question: Sign of W Suppose a fixed positively charged object (charge q s > 0) is at the origin and we move a negatively charged object (charge q 1 < 0) from A to B with r A < r B, where r is the distance from the origin. 1.Work done by the electrostatic force is positive and we do a positive amount of work 2.Work done by the electrostatic force is positive and we do a negative amount of work 3.Work done by the electrostatic force is negative and we do a positive amount of work 4.Work done by the electrostatic force is negative and we do a negative amount of work

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6 Concept Question Ans.: Sign of W W is the work done by the electrical force. This is the opposite of the work that we must do in order to move a charged object in an electric field due to source. The electrical force is attractive and we are moving the positively charged object away from the source (opposite the direction of the electric field). Answer 3: W is negative and we do a positive amount of work

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7 Group Problem: Work Done by Electrical Force A point-like charged source object (charge q s ) is held fixed. A second point-like charged object (charge q 1 )is initially at a distance r A from the fixed source and moves to a final distance r B from the fixed source. What is the work done by the electrical force on the moving object? Hint: What coordinate system is best suited for this problem?

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8 Sign of W: Negative Work Suppose a fixed positively charged source (charge q s > 0) is at the origin and a positively charged object (charge q 1 > 0) moves from A to B with r A > r B, where r is the distance from the origin, then W < 0.

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9 Work and Change in Kinetic Energy

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10 Group Problem: Work-Kinetic Energy In a Uniform Electric field Consider two thin oppositely uniform charged thin plates separated by a distance d. The surface charge densities on the plates are uniform and equal in magnitude. An electron with charge –e and mass m is released from rest at the negative plate and moves to the positive plate. What is the speed of the electron when it reaches the positive plate?

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11 Potential Energy Difference Suppose charged object s is fixed and located at the origin and charge object 1 moves from an initial position A, a distance r A from the origin to a final position B, a distance r B from the origin. The potential energy difference due to the interaction is defined to be the negative of the work done by the field in moving object 1 in from A to B. This is the same as the work you do in moving object 1 from A to B.

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12 Potential Energy: Zero Point Choose the zero point for the potential energy at infinity. Then set r A = ∞ and r B = r. The potential energy difference between ∞ and any point on a circle of radius r is

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13 Concept Question: Motion of Charged Objects Two oppositely charged are released from rest in an electric field. 1.Both charged objects will move from lower to higher potential energy. 2.Both charged objects will move from higher to lower potential energy. 3.The positively charged object will move from higher to lower potential energy; the negatively charged object will move from lower to higher potential energy. 4.The positively charged object will move from lower to higher potential energy; the negatively charged object will move from higher to lower potential energy.

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14 Concept Q. Ans.: Motion of Charged Objects 2. Both charged objects will move from higher to lower potential energy so that

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15 Configuration Energy What is the potential energy stored in a configuration of charged objects? Start with all the charged objects at infinity. Choose (1)Bring in the first charged object. (2)Bring in the second charged object (3)Bring in the third charged object (4)Configuration energy

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16 Group Problem: Build It How much energy does it take you to assemble the charges into the configuration at left, assuming they all started out an infinite distance apart?

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17 Electric Potential Difference Units: Joules/Coulomb = Volts Change in potential energy per test charge in moving the test object (charge q t ) from A to B:

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18 Demonstration Van de Graaf D29 Breakdown of dry air 33 kV/cm Video of Tesla Coil

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19 How Big is a Volt? AA Batteries1.5 VHigh Voltage Transmission Lines 100 kV-700 kV Car Batteries12 VVan der Graaf300 kV US Outlet (AC)120 VTesla Coil500 kV Distribution Power Lines 120 V- 70 kV Lightning MV

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20 E Field and Potential: Effects If you put a charged particle, (charge q), in a field: To move a charged particle, (charge q), in a field and the particle does not change its kinetic energy then:

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21 Concept Question: Motion of Charged Objects Two oppositely charged are released from rest in an electric field. 1.Both charged objects will move from lower to higher electric potential. 2.Both charged objects will move from higher to lower electric potential. 3.The positively charged object will move from higher to lower electric potential; the negatively charged object will move from lower to higher electric potential. 4.The positively charged object will move from lower to higher electric potential; the negatively charged object will move from higher to lower electric potential.

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22 Concept Q. Ans.: Motion of Charged Objects Two oppositely charged are released from rest in an electric field. 3. The positively charged object will move from higher to lower electric potential; the negatively charged object will move from lower to higher electric potential. For the positively charged object: For the negatively charged object:

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23 Potential & External Work Change in potential energy in moving the charged object (charge q) from A to B: Conservation of Energy Law:

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24 Demonstration Kelvin Water Drop in Wimshurst Machine in

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25 Demonstration: Kelvin Water

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26 Potential Created by Pt Charge Take V = 0 at r = ∞:

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27 Concept Question: Two Point Charges The work done in moving a positively charged object that starts from rest at infinity and ends at rest at the point P midway between two charges of magnitude +Q and –Q 1.is positive. 2.is negative. 3.is zero. 4.can not be determined – not enough info is given.

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28 Concept Question Answer: Two Point Charges The potential at ∞ is zero. The potential at P is zero because equal and opposite potentials are superimposed from the two point charges (remember: V is a scalar, not a vector) 3. Work from ∞ to P is zero.

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29 Potential Landscape Negative Charge Positive Charge

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30 Continuous Charge Distributions

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31 Continuous Charge Distributions Break distribution into infinitesimal charged elements of charge dq. Electric Potential difference between infinity and P due to d q. Superposition Principle: Reference Point:

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32 Calculating Electric Potential Difference for Continuous Distributions 1.Choose 2.Choose integration variables 3.Identify 4.Choose field point variables 5.Calculate source to field point distance 6.Define limits of integral 7.Integrate

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33 Worked Example Consider a uniformly charged ring with total charge Q. Find the electric potential difference between infinity and a point P along the symmetric axis a distance z from the center of the ring.

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34 Worked Example: Charged Ring Choose

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35 Group Problem A thin rod extends along the x-axis from x = -l /2 to x = l/2. The rod carries a uniformly distributed positive charge +Q. Calculate the electric potential difference between infinity and at a point P along the x-axis.

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