1. Charge Comes in + and – Is quantized Is conserved
elementary charge, e, is charge on 1 electron or 1 proton
e =  Coulombs
Is conserved
total charge remains constant

2. Milikan’s Experiment
By adjusting the voltage, a drop could be suspended.
Then FG = FE
Knowing density of oil, FG & total charge could be determined.
Finding lowest common denominator led to elementary charge.

3. Coulomb’s Law
F = kq1q2/r2
k = 8.99  109 N m2 / C2
q1, q2 are charges (C)
r2 is distance between the charges (m)
F is force (N) between charges
Applies directly to spherically symmetric charges

4. Electric Forces Mimic Gravitational Forces
Formulas are similar in structure
Both diminish exponentially with distance
Add vectors to determine total force on a charge
Difference: Electrical forces can be attractive or repulsive
Opposite electrical charges attract

5. Spherical Electric Fields
F =kqq0 r2
force
E = F = kq
q r2
field

6. Why use fields?
Forces exist only when two or more particles are present.
Fields exist even if no force is present. (Think gravity again!)
The field of one particle only at a time can be calculated.
Multiple particles create vector sums that yields resultant field

7. Field around + charge
Positive charges accelerate in direction of lines of force
Negative charges accelerate in opposite direction

8. Field around - charge Positive charges follow lines of force
Negative charges go in opposite direction

9. For any electric field E = F/q F: Electric Force in N
E: Electric Field in N/C
q: Charge in C

10. Principle of Superposition
When more than one charge contributes to the electric field, the resultant electric field is the vector sum of the electric fields produced by the various charges.

11. Field around dipole

12. Caution…
Electric field lines are NOT VECTORS, but may be used to derive the direction of electric field vectors at given points.
The resulting vector gives the direction of the electric force on a positive charge placed in the field.

13. Field Vectors

14. Electric Potential U = kqq0 r V = U = kq q0 r
potential energy
V = U = kq
q r
potential
(for spherically symmetric charges)

15. V = -Ed Electrical Potential V: change in electrical potential (V)
E: Constant electric field strength (N/m or V/m)
d: distance moved (m)

16. Electrical Potential Energy
U = qV
U: change in electrical potential energy (J)
q: charge moved (C)
V: potential difference (V)

17. Electrical Potential and Potential Energy
Are scalars!
(no direction)

18. Potential surfaces
high
highest
medium
low
lowest
positive
negative

19. Equipotential surfaces
high
low

20. Definition: Capacitor
Consists of two “plates” in close proximity.
When “charged”, there is a voltage across the plates, and they bear equal and opposite charges.
Stores electrical energy.

21. Capacitance C = q / DV C: capacitance in Farads (F)
q: charge (on positive plate) in Coulombs (C)
V: potential difference between plates in Volts (V)

22. UE = ½ C (DV)2 V: potential difference between plates (V)
Energy in a Capacitor
UE = ½ C (DV)2
U: electrical potential energy (J)
C: capacitance in (F)
V: potential difference between plates (V)

23. Capacitance of parallel plate capacitor
C = 0A/d
C: capacitance (F)
0 : permittivity (8.85 x F/m)
A: plate area (m2)
d: distance between plates(m)

24. Capacitors in Circuits+Q -Q +Q -Q

25. Equivalent Capacitance
series
Charge is same on all capacitors in series arrangement.
1/Ceq = 1/C1+ 1/C2 + 1/C3

26. Equivalent Capacitance
parallel
Voltage is same on all capacitors in parallel arrangement.
Ceq = C1+ C2 + C3

27. Parallel Plate Capacitor+Q -Q V1 V2 V3 V4 V5
dielectric E

28. Cylindrical Capacitor
- Q
+ Q E

29. Calculate the force on the 4.0 C charge due to the other two charges.
Problem #2
Calculate the force on the 4.0 C charge due to the other two charges.
+4 C
60o
60o
+1 C
+1 C

30. Calculate the mass of ball B, which is suspended in midair.
Problem #3
Calculate the mass of ball B, which is suspended in midair.
q = 1.50 nC A
R = 1.3 m
q = nC B

31. Problem #2 Two 5.0 C positive point charges are 1.0 m apart.
What is the magnitude and direction of the electric field at a point halfway between them?

32. Problem #4
Calculate the magnitude of the charge on each ball, presuming they are equally charged.
40o
1.0 m
1.0 m A B
0.10 kg
0.10 kg