1. Physics 1202: Lecture 3 Today’s Agenda
Announcements:
Lectures posted on:
HW assignments, solutions etc.
Homework #1:
On Masterphysics: due this coming Friday
Go to the syllabus and click on instructions to register (in textbook section).
Make sure to input oyur information to google form
Labs: Begin this week 1

2. Today’s Topic : Chapter 19: Gauss’s law
Examples …
Chapter 20: Electric energy & potential
Definition
How to compute them
Point charges
Equipotentials

3. Gauss’s Law Gauss’s law
electric flux through a closed surface is proportional to the charge enclosed by the surface:

4. Gauss’s Law Useful to get electric field Charged plate
symmetry: E ⏊ to plate
uniformly charged: s = q/A
So E: constant magnitude
Useful to get electric field
By taking advantage of geometry

5. Gauss’s law Charged line E ++++++++++++++++ x y Dx r' r DE
symmetry: E ⏊ to line
uniformly charged: l = q/L
So E: constant magnitude x y Dx r' r DE Dx DE
E ⏊ to end L
A=2pr L r

6. Geometries: Infinite Line of Charge
• Solution:
- symmetry: Ex=0
- sum over all elements x y Dx r' r Q DE Dq
= Q / L : linear charge
density
The Electric Field produced by an infinite line of charge is:
everywhere perpendicular to the line
is proportional to the charge density
decreases as 1/r.

7. Geometries: Infinite planey z Dx r' r Q DE Dq x Dy
• Solution:
- symmetry: Ex=Ey=0
- sum over all elements
= Q/A : surface charge density
The Electric Field produced by an infinite plane of charge is:
everywhere perpendicular to the plane
is proportional to the charge density
is constant in space !

8. About Two infinite planes ?
Same charge but opposite
Fields of both planes cancel out outside
They add up inside
Perfect to store energy !

9. Electric Field Distibutions
Summary
Electric Field Distibutions
Dipole
~ 1 / r3
Infinite
Plane of Charge
constant
Point Charge
~ 1 / r2
Infinite
Line of Charge
~ 1 / r

10. 20-1: Electric Potential Definitions Examples C B r A r qV Q
4pe0 r
4pe0 R
Definitions
Examples C B r B A r q A
equipotentials
path independence

11. Electric potential Energy
Recall 1201
Total mechanical energy
Constant for conservative forces
Potential energy U
Depends only on position (ex: U = mgy)
Change in U is independent of path
kinetic
potential
U2 , y2
U1 , y1

12. Electric potential Total energy is
Eini = Kini + Uini and Efin = Kfin + Ufin
Total energy is conserved
Conservative force

13. SI units: volt (V) with 1 V = 1 J/C
Electric potential
Recall from 1201: Work is: W = F Dx
But work-energy theorem: W = D K
So for conservative forces: D K = -D U
By analogy with electric field Þ
SI units: volt (V) with 1 V = 1 J/C

14. Energy Units Accelerators MKS: U = QV Þ 1 coulomb-volt = 1 joule
for particles (e, p, ...) eV = 1.6x10-19 joules
Accelerators
Electrostatic: VandeGraaff
electrons ® 100 keV ( 105 eV)
Electromagnetic: Fermilab
protons ® 1TeV ( eV)

15. - - - - - - - - - - - - - - - - - - - - - - - - - -
E from V?
We can obtain the electric field E from the potential V by inverting our previous relation between E and V:
Consider 2 plates and a charge q
force on q
Work done on q F +
But work-energy theorem
Conservative force

16. - - - - - - - - - - - - - - - - - - - - - - - - - -
E from V?
We can obtain the electric field E from the potential V by inverting our previous relation between E and V:
We have
So that F +
Therefore

17. X About V ? We found DV = Vfin - Vini . Can we define V alone ?
As for gravity, we set a reference point to zero
Ufin (yfin or Vfin)
Uini (yini or Vini)
Set to zero X

18. 20-2 Motion of Charged Particles in Electric Fields
Remember our definition of the Electric Field,
And remembering Physics 1201,
Now consider particles moving in fields.
Note that for a charge moving in a constant field
this is just like a particle moving near the
earth’s surface.
ax = ay = constant
vx = vox vy = voy + at
x = xo + voxt y = yo + voyt + ½ at2

19. Motion of Charged Particles in Electric Fields
Consider the following set up, e-
For an electron beginning at rest at the bottom plate, what will be its speed when it crashes into the top plate?
Spacing = 10 cm, E = 100 N/C, e = 1.6 x C, m = 9.1 x kg

20. Motion of Charged Particles in Electric Fields e-
vo = 0, yo = 0
vf2 – vo2 = 2aDx
Or,

21. Can use energy conservation
Recall: Eini = Kini + Uini and Efin = Kfin + Ufin
Energy conservation: Eini = Efin
but
as before !

22. Electric potential energy
20-3: Point charges
Gravitational force
Gravitational Potential energy U
By analogy: Þ
Electric force
Electric potential energy

23. Electric potential Energy
Meaning: recall
Total energy is conserved
Variation of U with r Þ variation of kinetic energy
For multiple charges
Simple sum
Ex: 3 charges q1 q3 q2
r13
r12
r23

24. Electric Potential Þ By analogy with the electric field
Defined using a test charge q0 Þ
We define a potential V due to a charge q
Using potential energy of a charge q and a test charge q0

25. Electric Potential
Define the electric potential of a point in space as the potential difference between that point and a reference point.
a good reference point is infinity ... we typically set V = 0
the electric potential is then defined as:
for a point charge, the formula is:

26. Lecture 3, ACT 1 ´ (a) VAB < 0 (b) VAB = 0 (c) VAB > 0 x -1mC A
A single charge ( Q = -1mC) is fixed at the origin. Define point A at x = + 5m and point B at x = +2m.
What is the sign of the potential difference between A and B? (VAB º VB - VA ) x
-1mC A B
(a) VAB < 0
(b) VAB = 0
(c) VAB > 0

27. Potential from N chargesx r1 r2 r3 q1 q3 q2
The potential from a collection of N charges is just the algebraic sum of the potential due to each charge separately. Þ

28. Þ Electric Dipole z +q r a -q1 2
The potential is much easier to calculate than the field since it is an algebraic sum of 2 scalar terms.
r2-r1
Rewrite this for special case r>>a: Þ
We can use this potential to calculate the E field of a dipole.
Must easier: using E = -DV /Dx … not here !

29. - - - - - - - - - - - - - - - - - - - - - - - - - -
20-4: Equipotentials
We can obtain the electric field E from the potential V by inverting our previous relation between E and V:
We found F
In general true for all direction +

30. 20-4: Equipotentials
Defined as: The locus of points with the same potential.
Example: for a point charge, the equipotentials are spheres centered on the charge.
GENERAL PROPERTY:
The Electric Field is always perpendicular to an Equipotential Surface.
Why??
Along the surface, there is NO change in V (it’s an equipotential!)
So, there is NO E component along the surface either… E must therefore be normal to surface

31. Equipotential Surfaces: examples
For two point charges:
© 2017 Pearson Education, Inc.

32. Conductors Claim Why?? Note+
Claim
The surface of a conductor is always an equipotential surface
(in fact, the entire conductor is an equipotential)
Why??
If surface were not equipotential, there would be an Electric Field component parallel to the surface and the charges would move!!
Note
Positive charges move from regions of higher potential to lower potential (move from high potential energy to lower PE).
Equilibrium means charges rearrange so potentials equal.

33. Charge on Conductors?
How is charge distributed on the surface of a conductor?
KEY: Must produce E=0 inside the conductor and E normal to the surface .
Spherical example (with little off-center charge):
E outside has spherical symmetry centered on spherical conducting shell. +
charge density induced on outer surface uniform
E=0 inside conducting shell. +q -
charge density induced on inner surface non-uniform.

34. A Point Charge Near Conducting Plane+ a q -
V=0

35. A Point Charge Near Conducting Planeq + a
The magnitude of the force is -
Image Charge
The test charge is attracted to a conducting plane

36. Equipotential Example
Field lines more closely spaced near end with most curvature .
Field lines ^ to surface near the surface (since surface is equipotential).
Equipotentials have similar shape as surface near the surface.
Equipotentials will look more circular (spherical) at large r.

37. Equipotential Surfaces & Electric Field
An ideal conductor is an equipotential surface
If two conductors are at the same potential, the one that is more curved will have a larger electric field around it
Think of Gauss’s law !
This is also true for different parts of the same conductor
Explains why more charges at edges

38. Applications: human body
There are electric fields inside the human body
the body is not a perfect conductor, so there are also potential differences.
An electrocardiograph plots the heart’s electrical activity
An electroencephalograph measures the electrical activity of the brain:

39. Recap of today’s lecture
Chapter 19: Gauss’s law
Examples …
Chapter 20: Electric energy & potential
Definition
How to compute them
Point charges
Equipotentials
Homework #1 on Mastering Physics
From Chapter 19
Due this Friday
Labs start this week