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MIDTERM 1 UTC 4.132 Thu-Sep 27, 7:00PM - 9:00PM Course Summary Unit 1 Provided Bring pencils, calculators (memory cleared) Slide 2 Chapter 17 Electric Potential Slide 3 The concept of electric field E deals with forces Electric potential > for work and energy Electric potential: electric potential energy per unit charge Practical importance: Reason about energy without having to worry about the details of some particular distribution of charges Batteries: provide fixed potential difference Predict possible pattern of E field Potential Energy To understand the dynamics of moving objects we used: forces, momenta, work, energy Slide 4 q1q1 For v U el > 0 for two like-sign charges (repulsion) q1q1 q2q2 q1q1 q2q2 U el < 0 for two unlike-sign Charges (attraction) Electric Potential Energy of Two Particles Slide 10 Potential energy = amount of work the two charges can do on each other when moved away from each other to Meaning of U 0 : r 12 Choose U 0 =0 no potential energy if r 12 (no interaction) q1q1 q2q2 q1q1 q2q2 Electric Potential Energy of Two Particles Slide 11 q1q1 q2q2 m1m1 m2m2 Electric and Gravitational Potential Energy Slide 12 Interaction between q 1 and q 2 is independent of q 3 There are three interacting pairs: q 1 q 2 q 2 q 3 q 3 q 1 U 12 U 23 U 31 U= U 12 + U 23 + U 31 Three Electric Charges Slide 13 q1q1 q6q6 q5q5 q4q4 q3q3 q2q2 Each (i,j) pair interacts: potential energy U ij Multiple Electric Charges Notation: i If q V < 0 then potential energy decreases and K increases If q V > 0 then potential energy increases and K decreases Sign of the Potential Difference Path 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. Slide 23 If freed, a positive charge will move to the area with a lower potential: V f V i < 0 (no external forces) V 1 < V 2 Moving in the direction of E means that potential is decreasing Sign of the Potential Difference Slide 24 To move a positive charge to the area with higher potential: V f V i > 0 V 1 < V 2 Need external force to perform work Moving opposite to E means that potential is increasing Sign of the Potential Difference Slide 25 Question 1 V 1 < V 2 A proton is free to move from right to left in the diagram shown. There are no other forces acting on the proton. As the proton moves from right to left, its potential energy: A)Is constant during the motion B)Decreases C)Increases D)Not enough information Slide 26 Potential Difference in a Nonuniform Field C x A to C: V 1 = -|E 1x |(x C -x A )C to B: V 2 = |E 2x |(x B -x C ); A to B: V = V 1 + V 2 = -|E 1x |(x C -x A ) + |E 2x |(x B -x C ) Slide 27 Potential Difference with Varying Field Slide 28 1. Along straight radial path: riri rfrf +q+q Example: Different Paths near Point Charge Origin at +q Slide 29 2. Special case iA: AB: BC: Cf:Cf: Example: Different Paths near Point Charge + Slide 30 3. Arbitrary path + Example: Different Paths near Point Charge