These notes are compiled by Jane Herron, Amanda Brixey and Kan Liu of Oklahoma School of Science and Mathematics, class of 98

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Chapter 24: Coulomb’s Law

I.                   Concepts and terms:

1)      Conservation of electric charge: total e-charge in a system remains const. You can transfer charge from one part to another.

2)      Conductors: atoms of the object have free e- moving around à disturbance

3)      Insulators: opposite of conductor

4)      Like charges repel, opposite charges attract

II.                Two ways to exchange charge:

1)      Direct Contact:  i.e. rubbing

2)      Induction:  i.e. bringing a charged item closer to another

III.             Electrical force between 2 charges:

Ø      Electric Force can be attractive or repulsive; magnetic force is only attractive

IV.              Superposition principle:

Ø                  Ftot = F2 + F3 + F4

# Chapter 25: Electric Field

v     Force-Field Map:

Ø                  F = kqQ / r2

v     E-Field Map:

Ø      E = kQ / r2

v     Electric Dipole:

Ø      P = qdx = charge x distance

v     Torque:

Ø      G = lever arm x Force => lever arm = l/2 sin q

v     E-Field: for infinity, long, linear charge dist.

v     Flux:

F = mass flux = kg/sec

v     Gauss’s Law:

v
E-fields of Conductors:

Ø      E = 0 inside a conductor

v     Infinite plane:

v     Infinite line charge:

v     Formulas for Area and Volume:

Sphere:           s = 4pr2                              Circle:             C = 2pr

V = 4/3 pr3                                         s = pr2

v     Charge densities:

Line (l) = Q / L

Sphere (s) = Q / A

Volume (r) = Q / V

# Chapter 26: Electric Potential

I.                   Work and Electric Potential Energy:

Ø      W = Fd = qEy       (F=qE and y =d)

* Use “sign” of q

Ø      Electric Potential Energy (U): U = qEy

Ø      Wa->b: Work done by field in moving q (test charge) from a to b.

Wa->b = qEya – qEyb = Ua - Ub

Ø
EPE of q in the presence of Q:

* Work done is path independent; it is conservative; depends on the endpoints.

II.                Electric Potential (V): EPE per unit charge

Wa->b = q(Va – Vb)

## III.             Work done in E-field:

### Equipotential Surfaces ^ to E-field lines

V.        Electron Volt (eV): amount of energy charge gains as travel through 1 V pot. change

W = q(Va  - Vb) = eV = Ua - Ub

1 eV = 1.6 x 10-19 J

Chapter 27: Capacitors and Dielectrics

I.      Capacitor: Conductor with charges on it (stores electric charge)

A.    Equations:

Unit: Farad (F) = Coulomb / Volt

2

V = dE V - V2 = ò1 Edr

II.   Capacitors in Series:

Ø     1/Ceq = 1/C1 + 1/C2 + …

Ø     Q same on each C, and V is different on each C

Ø     Vtotal = Q/Ceq

III. Capacitors in Parallel:

Ø      Ceq = C1 + C2 + …

Ø      Q is different on each C, and V is same on each C

Ø      Qtot = Q1 + Q2 = C1V + C2V = Vceq

IV. Energy in Charged Capacitor:

Ø       òdW = òdqV = òdqQ/C

Ø       U = ½ QV = ½ Q2/C = ½ CV2

Ø       W = U

V.    Energy density (u):

Ø      Potential Energy/Volume = U/dA

Ø      U = ½ eoE2

VI. Effect of Dielectric Material:

Ø      Separates metal conductors with small distance

Ø      Withstand stronger E-field => more charge stored

Ø      Increase capacitance

Ø      Voltage decreases when dielectric is inserted

Ø      E0 = V0 / d = s / e0 when empty

Ø      E = V/d = (s - sI)/ e0 with dielectric  => sI = s(k-1)/k

Ø      k = C(with di) / C0 (without di)

Ø      E0/E = k = s/(s-sI)

Ø      k = V0 / V

Ø      E = s/e      e = ke0 permitivity of dielectric

Ø      Qi = Q (k-1)/k

VII. Dielectric Strength:

Ø      Dielectric Strength: max E-field to withstand

Ø      Gauss’ Law   D: Electric Displacement = eE

Ø òDds = Qenclosed

Chapter 28: Current, Resistance, and Electromotive Force

I.  Current (I): Charge flow per time.

Ø      i = Dq/Dt or dq/dt

Ø      Unit: C/s = Ampere (A)

II.   Current density (j):

Ø      j = I / A                  Unit: Amp/m2

Ø      Dq = e- (AvDt)n

Ø      i = ne-vA                                        j = i/A = ne-vA/A =  ne-v = j

III. Resistivity (r):

Ø      r = E/j       Unit: W

Ø      Resistance = rl/A

Ø      V = EL = jrL = (pL)i/A

Ø      V = RI

IV. Electromotive Force (emf), e:

Ø      Moves “+” change from low potential to high potential

Ø      e = Vab­       open circuit

Ø      Vab = e - Ir  closed circuit

Ø      Current goes from “+” to “-“

V.    Rules for finding potential difference in closed circuit:

Ø     Potential drops add up to 0 once around circuit.

1)     Transverse resistor in direction of I: -iR

against direction of I:     +iR

2)     Transverse emf in direction of e:                  +e

against dirction of e: -e

VI. Power:

Ø      P = VabI                 Unit: Joule/sec = watts

Ø      P = RI2

Chapter 29: Direct-Current Circuits

I.      Series and Parallel Resistors:

Ø      Series:

Req = R1 + R2 + …

Vad = Vab + Vbc +Vcd

Vab = IR

Ø      Parrallel:

1/Req = 1/R1 + 1/R2 + …

I = I1 + I2 + I3 + …

II.   Kirchoff’s Rules:

Ø  Algebraic sum of currents to a branch = 0

III. Galvanometer: pivoted coil in magnetic field

1) Ammeter: connected in series with circuit

2) Voltmeter: connected in parallel with circuit

IV. RC circuit:

Ø     Initial (t=0)

a)     s is open => Q = 0

b)     s is closed => I = V/R

Ø final (t = ¥)

a)     I = 0

b)     Qf  = CV

Ø      Q = Qf (1 - e-t/RC)

Ø      t = RC = time constant : time that current falls to 1/e of I

Discharging (remove power supply):

Ø      q = Q0e-t/RC

Ø      I = I0e-t/RC

t = 0 => Q = Q0 => I = V/R = Q0/RC

t = ¥ => Q = 0 => I = 0