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

W_a->b = qEy_a – qEy_b = U_a - U_b

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

W_a->b = q(V_a – V_b)

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(V_a - V_b) = eV = U_a - U_b

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 = ò₁ Edr

II. Capacitors in Series:

Ø 1/C_eq = 1/C₁ + 1/C₂ + …

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

Ø V_total = Q/C_eq

III. Capacitors in Parallel:

Ø C_eq = C₁ + C₂ + …

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

Ø Q_tot = Q₁ + Q₂ = C₁V + C₂V = Vc_eq

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 e_oE²

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 - s_I)/ e₀ with dielectric => s_I = s(k-1)/k

Ø k = C_{(with di)} / C_{0 (without di)}

Ø E₀/E = k = s/(s-s_I)

Ø k = V₀ / V

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

Ø Q_i = Q (k-1)/k

VII. Dielectric Strength:

Ø Dielectric Strength: max E-field to withstand

Ø Gauss’ Law D: Electric Displacement = eE

Ø òDds = Q_enclosed

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 (