1. From last time(s)… Today… Gauss’ law
Conductors in electrostatic equilibrium
Today…
Finish conductors in electrostatic equilibrium
Work, energy, and (electric) potential
Electric potential and charge
Electric potential and electric field.
Oct. 2, 2008

2. Exam 1 Scores Class average = 76% (This is 84/110)
Your score posted at
Curve: B / BC boundary is 76%
Oct. 2, 2008

3. Conductor in Electrostatic Equilibrium
In a conductor in electrostatic equilibrium there is no net motion
of charge
E=0 everywhere inside the conductor
Ein
Conductor slab in an external field E: if E  0 free electrons would be accelerated
These electrons would not be in equilibrium
When the external field is applied, the electrons redistribute until they generate a field in the conductor that exactly cancels the applied field.
Etot =0
Etot = E+Ein= 0
Oct. 2, 2008

4. Conductors: charge on surface only
Choose a gaussian surface inside (as close to the surface as desired)
There is no net flux through the gaussian surface (since E=0)
Any net charge must reside on the surface (cannot be inside!)
E=0
Oct. 2, 2008

5. E-Field Magnitude and Direction
E-field always  surface:
Parallel component of E would put force on charges
Charges would accelerate
This is not equilibrium
Apply Gauss’s law at surface
this surface
this surface
this surface
Oct. 2, 2008

6. Summary of conductors everywhere inside a conductor
Charge in conductor is only on the surface
surface of conductor - +
Oct. 2, 2008

7. Electric forces, work, and energy
Consider positive particle charge q, mass m at rest in uniform electric field E
Force on particle from field
Opposite force on particle from hand
Let particle go - it moves a distance d
How much work was done on particle?
How fast is particle moving? +
Ask what happened to the energy.
v=0
v>0
Oct. 2, 2008

8. Work and kinetic energy
Work-energy theorem:
Change in kinetic energy of isolated particle = work done
Total work
In our case,
Oct. 2, 2008

9. Electric forces, work, and energy
Same particle, but don’t let go
How much force does hand apply?
Move particle distance d, keep speed ~0
How much work is done by hand on particle?
What is change in K.E. of particle?
Conservation of energy?
W stored in field as potential energy
Ask what happened to the energy. + +
Oct. 2, 2008

10. Work, KE, and potential energy
If particle is not isolated,
Work done on system
Change in kinetic energy
Change in electric potential energy
Works for constant electric field if
Only electric potential energy difference
Sometimes a reference point is chosen
E.g.
Then for uniform electric field
Oct. 2, 2008

11. Electric potential V
Electric potential difference V is the electric potential energy / unit charge = U/q
For uniform electric field,
This is only valid for a uniform electric field
Oct. 2, 2008

12. Quick Quiz
Two points in space A and B have electric potential VA=20 volts and VB=100 volts. How much work does it take to move a +100µC charge from A to B?
+2 mJ
-20 mJ
+8 mJ
+100 mJ
-100 mJ
Oct. 2, 2008

13. Check for uniform E-field
Push particle against E-field, or across E-field
Which requires work?
Constant electric potential in this direction + +
Ask what happened to the energy.
Increasing electric potential in this direction
Decreasing electric potential in this direction
Oct. 2, 2008

14. Potential from electric field
Potential changes largest in direction of E-field.
Smallest (zero) perpendicular to E-field
V=Vo
Oct. 2, 2008

15. Electric potential: general
Electric potential energy difference U proportional to charge q that work is done on
Electric potential difference
Depends only on charges that create E-fields
Electric field usually created by some charge distribution.
V(r) is electric potential of that charge distribution
V has units of Joules / Coulomb = Volts
Oct. 2, 2008

16. Electric potential of point charge
Electric field from point charge Q is
What is the electric potential difference?
Define
Then
for point charge
Oct. 2, 2008

17. Electric Potential of point charge
Potential from a point charge
Every point in space has a numerical value for the electric potential
Distance from ‘source’ charge +Q y +Q x
Oct. 2, 2008

18. Potential energy, forces, work
Electric potential energy=qoV A B
qo > 0
U=qoV
Point B has greater potential energy than point A
Means that work must be done to move the test charge qo from A to B.
This is exactly the work to overcome the Coulomb repulsive force.
Work done = qoVB-qoVA =
Differential form:
Oct. 2, 2008

19. V(r) from multiple charges
Work done to move single charge near charge distribution.
Other charges provide the force, q is charge of interest. q1 q2 q q3
Superposition of individual electric potentials
Oct. 2, 2008

20. Quick Quiz 1 A B Both A and B Neither of them
At what point is the electric potential zero for this electric dipole? +Q -Q
x=+a
x=-a A B A B
Both A and B
Neither of them
Oct. 2, 2008

21. Superposition: the dipole electric potential+Q -Q
x=+a
x=-a
Superposition of
potential from +Q
potential from -Q + =
V in plane
Oct. 2, 2008