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: Coulombs 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 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:


 


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

IV.              Superposition principle:

 


                  Ftot = F2 + F3 + F4

 

 


Chapter 25: Electric Field

 

v     Force-Field Map:


 


                  F = kqQ / r2

 

v     E-Field Map:


 


      E = kQ / r2

 

 

v     Electric Dipole:


 

 


      P = qdx = charge x distance

 

v     Torque:


 


      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     Gausss Law:


 

 


v    

E-fields of Conductors:

 


      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:

      W = Fd = qEy (F=qE and y =d)

 

* Use sign of q

      Electric Potential Energy (U): U = qEy

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

Wa->b = qEya qEyb = Ua - Ub

     

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:

 

 


IV. Potential Gradient:


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 V1 - V2 = 1 Edr

II.   Capacitors in Series:

     1/Ceq = 1/C1 + 1/C2 +

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

     Vtotal = Q/Ceq

 

III. Capacitors in Parallel:

      Ceq = C1 + C2 +

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

      Qtot = Q1 + Q2 = C1V + C2V = Vceq

 

IV. Energy in Charged Capacitor:

       dW = dqV = dqQ/C

       U = QV = Q2/C = CV2

       W = U

 

V.    Energy density (u):

      Potential Energy/Volume = U/dA

      U = eoE2

 

VI. Effect of Dielectric Material:

      Separates metal conductors with small distance

      Withstand stronger E-field => more charge stored

      Increase capacitance

      Voltage decreases when dielectric is inserted

      E0 = V0 / d = s / e0 when empty

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

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

      E0/E = k = s/(s-sI)

      k = V0 / V

      E = s/e e = ke0 permitivity of dielectric

      Qi = Q (k-1)/k

VII. Dielectric Strength:

      Dielectric Strength: max E-field to withstand

      Gauss Law D: Electric Displacement = eE

Dds = Qenclosed

 

Chapter 28: Current, Resistance, and Electromotive Force

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

      i = Dq/Dt or dq/dt

      Unit: C/s = Ampere (A)

 

II.   Current density (j):

      j = I / A Unit: Amp/m2

      Dq = e- (AvDt)n

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

III. Resistivity (r):

      r = E/j Unit: W

      Resistance = rl/A

      V = EL = jrL = (pL)i/A

      V = RI

 

IV. Electromotive Force (emf), e:

      Moves + change from low potential to high potential

      e = Vab open circuit

      Vab = e - Ir closed circuit

      Current goes from + to -

 

V.    Rules for finding potential difference in closed circuit:

     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:

      P = VabI Unit: Joule/sec = watts

      P = RI2

 

Chapter 29: Direct-Current Circuits

I.      Series and Parallel Resistors:

      Series:

Req = R1 + R2 +

Vad = Vab + Vbc +Vcd

Vab = IR

 

      Parrallel:

1/Req = 1/R1 + 1/R2 +

I = I1 + I2 + I3 +

 

II.   Kirchoffs Rules:

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:

     Initial (t=0)

a)     s is open => Q = 0

b)     s is closed => I = V/R

final (t = )

a)     I = 0

b)     Qf = CV

      Q = Qf (1 - e-t/RC)

 

      t = RC = time constant : time that current falls to 1/e of I0

 

Discharging (remove power supply):

      q = Q0e-t/RC

      I = I0e-t/RC

 


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

t = => Q = 0 => I = 0