MIDTERM 1 UTC Thu-Sep 27, 7:00PM - 9:00PM Course Summary Unit 1 Provided Bring pencils, calculators (memory cleared)

Chapter 17 Electric Potential

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

q1q1 For v<<c: A single particle has no (electric) potential energy Energy of a Single Particle Kinetic energy is associated with motion The energy of a single particle with charge q 1 consists solely of its particle energy. Particle energyKinetic energy Rest energy The kinetic energy of a single particle can be changed if positive or negative work is done on the particle by its surroundings.

q1q1 q2q2 r 12 Energy of the system: 1.Energy of particle q 1 2.Energy of particle q 2 3.Interaction energy U el E system = E 1 +E 2 +U el To change the energy of particles we have to perform work. W ext – work done by forces exerted by other objects W int – work done by electric forces between q 1 and q 2 Q – thermal transfer of energy into the system Electric Potential Energy of Two Particles Potential energy is associated with pairs of interacting objects

q1q1 q2q2 r 12  U el  -W int Total energy of the system can be changed (only) by external forces or by adding (thermal) energy. Work done by internal forces: Electric Potential Energy of Two Particles if

q1q1 q2q2 r 12 Electric Potential Energy of Two Particles F int

q1q1 q2q2 r 12 The potential energy of a pair of particles is: Electric Potential Energy of Two Particles F int

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

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

q1q1 q2q2 m1m1 m2m2 Electric and Gravitational Potential Energy

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

q1q1 q6q6 q5q5 q4q4 q3q3 q2q2 Each (i,j) pair interacts: potential energy U ij Multiple Electric Charges Notation: i<j avoids double counting: ij, ji

Electric potential  electric potential energy per unit charge Units: J/C = V (Volt) Electric potential – often called potential Electric potential difference – often called voltage Electric Potential Volts per meter = Newtons per Coulomb Alessandro Volta ( )

Single charge has no electric potential energy Single charge has potential to interact with other charge – it creates electric potential probe charge q2q2 V due to One Particle J/C, or Volts Electric potential at B due to charge q 1.

q3q3 Electric potential is scalar: Electric potential energy of the system: If we add one more charge at position C: V due to Two Particles

r , V=0 Negative charge Positive charge V at Infinity

What is the electrical potential at a location 1Å from a proton? What is the potential energy of an electron at a location 1Å from a proton? 1Å1Å Exercise

What is the change in potential in going from 1Å to 2Å from the proton? 1Å1Å 2Å2Å What is the change in electric potential energy associated with moving an electron from 1Å to 2Å from the proton? Does the sign make sense? Exercise

Electric potential  electric potential energy per unit charge Electric Potential Difference in a Uniform Field

Example 30 0

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.

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

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

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

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 )

Potential Difference with Varying Field

1. Along straight radial path: riri rfrf +q+q Example: Different Paths near Point Charge Origin at +q

2. Special case iA: AB: BC: Cf:Cf: Example: Different Paths near Point Charge +

3. Arbitrary path + Example: Different Paths near Point Charge