Question 1

MIDTERM 1

UTC 4.132 Thu-Sep 27, 7:00PM - 9:00PMCourse Summary Unit 1 ProvidedBring pencils, calculators (memory cleared)Chapter 17Electric Potential2The concept of electric field E deals with forcesElectric potential > for work and energy Electric potential: electric potential energy per unit chargePractical importance:Reason about energy without having to worry about the details of some particular distribution of chargesBatteries: provide fixed potential differencePredict possible pattern of E fieldPotential EnergyTo understand the dynamics of moving objects we used:forces, momenta, work, energy3

q1

For v 0 for two like-sign charges(repulsion)

q1

q2

q1

q2Uel < 0 for two unlike-sign Charges (attraction)

Electric Potential Energy of Two Particles9

Potential energy = amount of work the two charges can do on each other when moved away from each other to

Meaning of U0:r12

Choose U0=0 no potential energy if r12(no interaction)

q1

q2

q1

q2Electric Potential Energy of Two Particles10

q1

q2

m1m2

Electric and Gravitational Potential Energy11

Interaction between q1 and q2 is independent of q3There are three interacting pairs:q1 q2q2 q3q3 q1U12U23U31U= U12+ U23+ U31

Three Electric Charges12

q1

q6

q5

q4

q3

q2Each (i,j) pair interacts:potential energy Uij

Multiple Electric ChargesNotation: i 0 then potential energy increases and K decreasesSign of the Potential DifferencePath going in the direction of E: Potential is decreasing (V < 0)

Path going opposite to E: Potential is increasing (V > 0)

Path going perpendicular to E: Potential does not change (V = 0)

The potential difference V can be positive or negative.The sign determines whether a particular charged particle will gain or lose energy in moving from one place to another.22

If freed, a positive charge will move to the area with a lower potential:Vf Vi < 0

(no external forces)V1 < V2Moving in the direction of E means that potential is decreasingSign of the Potential Difference23So if the potential energy decreases, K must increase since there are no external forces in this problem. What if instead, we freed a negative charge? Would it move to higher or lower potential? Would its potential energy increase or decrease?

To move a positive charge to the area with higher potential:Vf Vi > 0

V1 < V2Need external force to perform workMoving opposite to E means that potential is increasingSign of the Potential Difference24What can we say about the protons kinetic energy?Question 1

V1 < V2A proton is free to move from right to leftin the diagram shown. There are no other forces acting on the proton. As the proton moves from right to left, its potential energy:Is constant during the motionDecreasesIncreasesNot enough informationPotential Difference in a Nonuniform Field

CxA to C: DV1 = -|E1x|(xC-xA) C to B: DV2 = |E2x|(xB-xC); A to B: DV = DV1+ DV2 = -|E1x|(xC-xA) + |E2x|(xB-xC)26Potential Difference with Varying Field

1. Along straight radial path:

rirf

+qExample: Different Paths near Point Charge

Origin at +q28For final r greater than initial r, the change in potential is less than zero as expected since the path direction is the same as that of the electric field. Likewise, if we go from a larger r to a small r, the potential increases.2. Special case

iA:

AB:

BC:

Cf:

Example: Different Paths near Point Charge

+293. Arbitrary path

+Example: Different Paths near Point Charge30