Question 1 A.a uniformly charged long rod. B.a uniformly charged ring. C.a uniformly charged disk. D.a point charge. Which one of these statements is true? When near the center of the object, the electric field hardly changes with increasing distance from

Question A.The electric field inside both balls is zero. B.The electric field inside the metal ball is zero, but it is nonzero inside the plastic ball. C.The electric fields inside both objects are nonzero and are pointing toward each other. D.The electric field inside the plastic ball is zero, but it is nonzero inside the metal ball. A solid metal ball carrying negative excess charge is placed near a uniformly charged plastic ball. Which one of the following statements is true? -Q+Q metalplastic

Question A.The electric field of a very long uniformly charged rod has a 1/r distance dependence. B.The electric field of a capacitor at a location outside the capacitor is very small compared to the field inside the capacitor. C.The fringe field of a capacitor at a location far away from the capacitor looks like an electric field of a point charge. D.The electric field of a uniformly charged thin ring at the center of the ring is zero. Which one of these statements is false?

Chapter 17 Electric Potential

The concept of electric field E deals with forces Introduce 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

F 2,surr f 2,1 f 1,2 f 2,3

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

q1q1 q2q2 r 12  U el  -W int Total energy of the system can be changed (only) by external forces. Work done by internal forces: Electric Potential Energy of Two Particles Energy of the system:1.Energy of particle q 1 2.Energy of particle q 2 3.Interaction energy U el To change the energy of particles we have to perform work. if: Energy Principle for a multiparticle system.

Example = (1.6x C)(2x10 3 N/C)(0.004m) =1.3x J  K  U electric = -1.3x J x

Electric potential  electric potential energy per unit charge Units: J/C = V (Volt) Electric potential, V – often called potential Electric potential difference,  V – often called voltage Electric Potential Difference in a Uniform Field Volts per meter = Newtons per Coulomb

If we multiply through by q, we recover the relation between the change in potential energy and work done on q by the internal force.

Example 30 0

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

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

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 2 > V 1 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

Question 2 V 1 < V 2 A system consists of a proton inside of a capacitor. The proton moves from left to right as shown at a constant speed due to the action of an external agent. Which of the following statements is true? A)The proton’s potential energy is unchanged and the external agent does no work on the system. B)The proton’s potential energy decreases and the external agent does work W > 0 on the system. C)The proton’s potential energy decreases and the external agent does work W < 0 on the system. D)The proton’s potential energy increases and the external agent does work W < 0 on the system. E)The proton’s potential energy increases and the external agent does work W > 0 on the system.

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

i f dl F For very short path: Example: E = N/C,  l = 1 mm: Potential Difference and Electric 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