Question 1

Question 1a uniformly charged long rod.a uniformly charged ring.a uniformly charged disk.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 from1CQuestionThe 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.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+Qmetalplastic2Answer: BQuestionThe 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. Which one of these statements is false?3Answer: CChapter 17Electric Potential4The concept of electric field E deals with forcesIntroduce electric 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, energy5

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 Particles12

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 Particles13

q1

q2

m1m2

Electric and Gravitational Potential Energy14

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

Three Electric Charges15

q1

q6

q5

q4

q3

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

Multiple Electric ChargesNotation: i x_i, we move from right to left. In the picture shown, delta_y < 0 since y_2 < y_1, so in general, delta_l vector = idx + jdy + k dz.26Example

300

r, V=0V at InfinityrVPositive charge

28

Uel > 0 for two like-sign charges(repulsion)

q1

q2

q1

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

Electric Potential Energy of Two Particles29If qV < 0 then potential energy decreases and K increasesIf qV > 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.30

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 Difference31So 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

V2 > V1Need external force to perform workMoving opposite to E means that potential is increasingSign of the Potential Difference32What 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 informationQuestion 2

V1 < V2 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?The protons potential energy is unchanged and the external agent does no work on the system.The protons potential energy decreases and the external agent does work W > 0 on the system.The protons potential energy decreases and the external agent does work W < 0 on the system.The protons potential energy increases and the external agent does work W < 0 on the system.The protons potential energy increases and the external agent does work W > 0 on the system.E. 34Potential 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)35Potential Difference with Varying Field

ifdlF

For very short path:

Example: E = 3.106 N/C, l = 1 mm:

Potential Difference and Electric Field37

1. Along straight radial path:

rirf

+qExample: Different Paths near Point Charge

Origin at +q38For 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

+393. Arbitrary path

+Example: Different Paths near Point Charge40