1. Coulomb’s Law
Charges with the same sign repel each other, and charges with opposite signs attract each other.
The electrostatic force between two particles is proportional to the amount of electric charge that each possesses and is inversely proportional to the distance between the two squared. q1 q2 r
by 1 on 2
1,2
1,2
1,2
Coulomb constant:
where e0 is called the permittivity constant.

2. Electric Field
Define electric field, which is independent of the test charge, q2 , and depends only on position in space:
Electric Field due to a Point Charge Q

3. Dynamics of a Charged Mass in Electric Field
For -Q<0 in uniform E downward: -Q
Oscilloscope
Ink-Jet Printing
vy = at = qE/m t vx >>0
Oil drop experiment

4. Electric Field from Coulomb’s Law+ -
Bunch of Charges
Continuous Charge Distribution dq P P k
(volume charge)
(surface charge)
(line charge)
Summation over discrete charges
Integral over continuous charge distribution

5. Gauss’s Law: Quantitative Statement
The net electric flux through any closed surface equals the net charge enclosed by that surface divided by ε0.
How do we use this equation??
The above equation is TRUE always but it doesn’t
look easy to use.
BUT - It is very useful in finding E when the physical situation exhibits a lot of SYMMETRY.

6. Charges and fields of a conductor
In electrostatic equilibrium, free charges inside a conductor do not move. Thus, E = 0 everywhere in the interior of a conductor.
Since E = 0 inside, there are no net charges anywhere in the interior. Net charges can only be on the surface(s).
The electric field must be perpendicular to the surface just outside a conductor, since, otherwise, there would be currents flowing along the surface.

7. Electric Potential Energy of a Charge in Electric Field
Coulomb force is conservative
=> Work done by the Coulomb force is path independent.
Can associate potential energy
to charge q0 at any point r in space.
It’s energy! A scalar measured in J (Joules)

8. Electric Potential Scalar! taking the same reference point
U(r) of a test charge q0 in electric field generated by other source charges is proportional to q0 .
So U(r)/q0 is independent of q0, allowing us to introduce electric potential V independent of q0.
taking the same reference point
[Electric potential] = [energy]/[charge]
SI units: J/C = V (volts)
Scalar!
A positively charged particle produces a positive electric potential; a negatively charged particle produces a negative electric potential.
Potential energy difference when 1 C of charge is moved between points of potential difference 1 V

9. E from V
We can obtain the electric field E from the potential V by inverting the integral that computes V from E:
Expressed as a vector, E is the negative gradient of V

10. Electric Potential Energy and Electric Potential
positive charge
High U (potential energy)
Low U
High V
Low V
Electric field direction
High V (potential)
Low V
Electric field direction
negative charge
High U
Low U

11. Two Ways to Calculate Potential
Integrate -E from the reference point at (∞) to the point (P) of observation: Q P r
A line integral (which could be tricky to do)
If E is known and simple and a simple path can be used, it may be reduced to a simple, ordinary 1D integral.
Integrate dV (contribution to V(r) from each infinitesimal source charge dq) over all source charges: q1 q2 q3 q4 P P Q

12. Capacitance The two conductors hold charge +Q and –Q, respectively.
Capacitor plates hold charge Q
The two conductors hold charge +Q and –Q, respectively.
The capacitance C of a capacitor is a measure of how much charge Q it can store for a given potential difference ΔV between the plates.
Expect
Capacitance is an intrinsic property of the capacitor.
farad
(Often we use V to mean ΔV.)

13. Steps to calculate capacitance C
Put charges Q and -Q on the two plates, respectively.
Calculate the electric field E between the plates due to the charges Q and -Q, e.g., by using Gauss’s law.
Calculate the potential difference V between the plates due to the electric field E by
Calculate the capacitance of the capacitor by dividing the charge by the potential difference, i.e., C = Q/V.

14. Energy of a charged capacitor
How much energy is stored in a charged capacitor?
Calculate the work required (usually provided by a battery) to charge a capacitor to Q
Calculate incremental work dW needed to move charge dq from negative plate to the positive plate at voltage V.
Total work is then

15. Dielectrics between Capacitor Plates
+ Q
- Q
free charges
Electric field E between plates can be calculated from Q – q.
neutral -q +q
Polarization
Charges ± q
The presence of a dielectric weakens the electric field, therefore weaken the potential drop between the plates, and leads to a large capacitance.

16. Capacitors in Parallel
V is common
Equivalent Capacitor:
where

17. Capacitors in Series
q is common
Equivalent Capacitor:
where

18. Electric Current Magnitude
Current = charges in motion
Magnitude
rate at which net positive charges move across a cross sectional surface
J = current density (vector) in A/m²
Units: [I] = C/s = A (ampere)
Current is a scalar, signed quantity, whose sign corresponds to the direction of motion of net positive charges by convention

19. Ohm’s Law and non linear devices
Current-Potential (I-V) characteristic of a device may or may not obey Ohm’s Law:
or V = IR with R constant
Resistance
(ohms)
gas in fluorescent tube
tungsten wire
diode

20. Energy in Electric Circuits
Steady current means a constant amount of charge ΔQ flows past any given cross section during time Δt, where I= ΔQ / Δt.
Energy lost by ΔQ is V
=> heat
Read 27-8 (semi-conductor) and 27-9 (superconductor)
So, Power dissipation = rate of decrease of U =

21. Resistors in Parallel Devices in parallel has the same potential drop
Generally,
•••

22. Kirchhoff’s Rules Kirchhoff’s Rule 1: Loop Rule
When any closed loop is traversed completely in a circuit, the algebraic sum of the changes in potential is equal to zero.
Coulomb force is conservative
Kirchhoff’s Rule 2: Junction Rule
The sum of currents entering any junction in a circuit is equal to the sum of currents leaving that junction.
Conservation of charge
In and Out branches
Assign Ii to each branch

23. Loop current example (with parallel R combos)
Sketch the diagram
Simplify using equivalent resistors
Label loop currents with directions
Use Loop currents I1 and I2
Choose interior clockwise loops
. Set up cononical equations in
. I1 I Ε format
I1 -I2
Replace by equivalent R=2Ω first.
I1 (12 +6) +I2 (-6) = +18 (Emf) Left loop
I1 (-6) + I2 (6+3+2) =+21 (Emf) Right loop
Note Symmetry of Equations

24. Galvanometer Inside Ammeter and Voltmeter
Galvanometer: a device that detects small currents and indicates its magnitude. Its own resistance Rg is small for not disturbing what is being measured.
shunt resistor
galvanometer
Ammeter: an instrument used to measure currents
Voltmeter: an instrument used to measure potential differences
galvanometer

25. Discharging a Capacitor in RC Circuits
Switch closed at t=0. Initially C is fully charged with Q0
Loop Rule: I
Convert to a differential equation
Solve it!

26. Charging a Capacitor in RC Circuits
Switch closed at t=0
C initially uncharged, thus zero voltage across C.
Loop Rule:
3. Convert to a differential equation
Solve it!
(τ=RC is the time constant again)