1. Exam 1 on Feb 17 (Tuesday), 8-9:30 PM, PHYS Rm 112.

2. Which arrow best represents the field at the “X”?
Clicker Question 1
Which arrow best represents the field at the “X”? A) B) E
C) E=0 D) E)

3. Question 2 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.
Answer: C It looks like a dipole field! 8

4. Infinitesimals and Integrals in Science
Charge distribution is not continuous Q
Charge distribution is not exactly uniform
Mathematical idealization
Works well for macroscopic systems
Atomic force microscope: scans microscopic structure using variations in charge density on surface

5. Chapter 17
Electric Potential

6. Electric and Gravitational Potential Energyq1 q2 m1 m2

7. 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
E = 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 q1 and q2
Q – thermal transfer of energy into the system

8. Electric Potential Energy of Two Particlesq2
r12
Uel  -Wint q1 if
Total energy of the system can be changed (only) by external forces.
Scalar product of 2 vectors! F here is the force between two charged particles, ie, the Coulomb force.
Work done by internal forces:

9. Electric Potential Energy of Two Particles
Fint q2
r12 q1
We will treat the charges as if they are like-sign particles. Thus, F is a repulsive force and the displacement due to F is along the dr direction. If the charges were of opposite sign, F would point from 2 to 1 and the displacement of 2 would again be in the F direction. Thus, the dot product is a positive quantity in either case.

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

11. Electric Potential Energy of Two Particlesq2 q2 q1 q1
Uel > 0 for two like-sign charges
(repulsion)
Uel < 0 for two unlike-sign
Charges (attraction)

12. Electric and Gravitational Potential Energyq1 q2 m1 m2

13. Three Electric Charges
Interaction between q1 and q2 is independent of q3
There are three interacting pairs:
q1  q2
q2  q3
q3  q1
U12
U23
U31
U= U12+ U23+ U31

14. Multiple Electric Chargesq1 q3 q6
Each (i,j) pair interacts:
potential energy Uij q2 q5 q4

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

16. V due to One Particle Single charge has no electric potential energyq2
Single charge has potential to interact with other charge –
it creates electric potential
probe charge
J/C, or Volts

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

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

19. 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?

20. 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?

21. 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

22. If we multiply each side of the equation by q, we recover the relation between the change in potential energy and work done by internal force on q. Delta_x = x_f – x_i. If x_f > 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.
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.

23. Example
300

24. Example x
An electron traveling to the right enters capacitor through a small hole
at A. Electric field strength is 2x103 N/C. What is the change in the
electron’s potential energy in traveling from A to B? What is its
change in kinetic energy? D(AB)= 4mm
The system is comprised of the charged capacitor plates and the electron. this example, the electric force is in the direction opposite to the displacement through which the force acts. Remember that e is a number. Also remember that the F in this expression is that due to sources within the system (F_internal).
= (1.6x10-19 C)(2x103 N/C)(0.004m) =1.3x10-18 J
DK = -DUelectric = -1.3x10-18 J

25. Sign of the Potential Difference
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 qV < 0 – then potential energy decreases and K increases
If qV > 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)

26. 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

27. 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)
So if the potential energy decreases, K must increase since there are no external forces in this problem.
V1 < V2
Moving in the direction of E means that potential is decreasing

28. 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
What can we say about the proton’s kinetic energy?
V1 < V2
Moving opposite to E means that potential is increasing