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

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

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

**Chapter 17** Electric Potential

**Potential Energy** To understand the dynamics of moving objects we used: forces, momenta, work, energy The concept of electric field Edeals 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

**Energy of a Single Particle** q1 Particle energy Kinetic energy Rest energy For v<<c: The energy of a single particle with charge q1 consists solely of its particle energy. Kinetic energy is associated with motion A single particlehas no (electric) potential energy The kinetic energy of a single particle can be changed if positive or negative work is done on the particle by its surroundings.

**Electric Potential Energy of Two Particles** Potential energy is associated with pairs of interacting objects Energy of the system: • Energy of particle q1 • Energy of particle q2 • Interaction energy Uel q2 r12 q1 Esystem = E1+E2+Uel To change the energy of particles we have to perform work. Wext – work done by forces exerted by other objects Wint – work done by electric forces between q1and q2 Q – thermal transfer of energy into the system

**Electric Potential Energy of Two Particles** if q2 r12 Uel -Wint q1 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** Fint q2 r12 q1

**Electric Potential Energy of Two Particles** Fint q2 r12 q1 The potential energy of a pair of particles is:

**Electric Potential Energy of Two Particles** q2 q2 q1 q1 Uel > 0 for two like-sign charges (repulsion) Uel < 0 for two unlike-sign Charges (attraction)

**Electric Potential Energy of Two Particles** q2 q2 q1 q1 r12 Meaning of U0: Choose U0=0 – no potential energy if r12 (no interaction) Potential energy = amount of work the two charges can do on each other when moved away from each other to

**Electric and Gravitational Potential Energy** q2 m2 q1 m1

**Three Electric Charges** Interaction betweenq1andq2is independent of q3 There are three interacting pairs: q1 q2 q2 q3 q3 q1 U12 U23 U31 U= U12+ U23+ U31

**Multiple Electric Charges** q1 q3 q6 q2 q5 q4 Each (i,j) pair interacts: potential energyUij Notation: i<j avoids double counting: ij, ji

**Electric Potential** Alessandro Volta (1745 - 1827) Electric potential electric potential energy per unit charge Units: J/C = V (Volt) Volts per meter = Newtons per Coulomb Electric potential – often called potential Electric potential difference – often called voltage

**V due to One Particle** q2 Single charge hasnoelectric potential energy Single charge haspotentialto interact with other charge – it creates electric potential probe charge J/C, or Volts Electric potential at B due to charge q1.

**V due to Two Particles** q3 Electric potential is scalar: Electric potential energy of the system: If we add one more charge at position C:

**V at Infinity** r, V=0 Positive charge Negative charge

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

**Exercise** 2Å 1Å What is the change in potential in going from 1Å to 2Å from the proton? 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?

**Electric Potential Energy of Two Particles** q2 r12 q1 if : Energy of the system: • Energy of particle q1 • Energy of particle q2 • Interaction energy Uel To change the energy of particles we have to perform work. Energy Principle for a multiparticle system. Uel -Wint Total energy of the system can be changed (only) by external forces. Work done by internal forces:

**Example** The electron enters the capacitor through a small hole at A with an initial velocity to the right. What is the change in the electron’s potential energy in traveling from A to B? Change in kinetic energy? D(AB)= 4mm; 2x103N/C. x = (1.6x10-19 C)(2x103 N/C)(0.004m) =1.3x10-18 J DK = -DUelectric = -1.3x10-18 J

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

**Example** 300

**V at Infinity** r, V=0 Positive charge V r

**Electric Potential Energy of Two Particles** q2 q2 q1 q1 Uel > 0 for two like-sign charges (repulsion) Uel < 0 for two unlike-sign Charges (attraction)

**Sign of the Potential Difference** If qV < 0 – then potential energy decreases and K increases If qV > 0 – then potential energy increases and K decreases 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.

**Sign of the Potential Difference** If freed, a positive charge will move to the area with a lower potential: Vf – Vi < 0 (no external forces) V1 < V2 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: Vf – Vi > 0 Need external force to perform work V2 > V1 Moving opposite to E means that potential is increasing

**Question 1** 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: Is constant during the motion Decreases Increases Not enough information V1 < V2

**Potential Difference in a Nonuniform Field** C x Ato C: DV1 = -|E1x|(xC-xA) Cto B: DV2 = |E2x|(xB-xC); Ato B: DV= DV1+ DV2 = -|E1x|(xC-xA) + |E2x|(xB-xC)

**Potential Difference with Varying Field**

**Example: Different Paths near Point Charge** 1. Along straight radial path: rf ri Origin at +q +q

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

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