Lecture 8 Physics 2018/2019 Baghdad Battery or Parthian Battery ceramic pot, tube of one metal and a rod of another metal Khujut Rabu, Iraq,
Ctesiphon the capital of Parthian (150 BC-223 copper AD) or Sasanian (224-650 AD) empires
Luigi Aloisio Galvani Alessandro Giuseppe (1737 –1798) Antonio Anastasio Animal electricity Volta (1745 – 1827) Electrochemical reaction Electricity, electric charge
• Positive and negative charge (electron, proton, positron, anti-proton, etc.) • charge [Q]= 1 C (coulomb) - +
• SI unit: 1C=1A(ampere)1s (second)
• Quantitized 푞 = ±푛 푒 푒 = 1.602푥10−19퐶
• Unlike charge – attract
- +
Like charge – repel
- - + + CONSERVATION OF CHARGE: The net electric charge (algebraic) of an isolated system does not change, no matter what interactions occur within the system. We must add the charges algebraically, with due regard for their signs.
symbol mass [kg] charge [e] proton p 1.6726·10-27 +e neutron n 1.6749·10-27 0 elektron e 9.11 ·10 – 31 -e Coulomb’s law – force of attraction F<0 or repulsion F>0
1 푞 푞 1 퐹 = 1 2 푘 = 4휋휀 푟2 4휋휀 qi – charge 휀 = 휀0휀푟 푝푒푟푚𝑖푡𝑖푣𝑖푡푦 표푓 푣푎푐푢푢푚 푎푛푑 푟푒푙푎푡𝑖푣푒 푝푒푟푚𝑖푡𝑖푣𝑖푡푦 Charles-Augustin −12 −1 2 −1 −2 de Coulomb 휀0 = 8,854187푥10 퐹푚 (퐶 푁 푚 ) Newton’s law of universal gravitation (1736-1806) 퐻+ + attraction only! 퐻+ 퐻+ 퐻 + + + + 푚1푚2 1 퐹 = 휅 2 푟 푘0 = −12 휅 = 6,674푥10 −11푁푚2푘푔−2 4푥 3,14푥8,854푥10 푘 = 8,988푥10 9푁푚 2퐶−2 −3 0 1,008푥10 −27 푚 + = 푘푔 = 1,67푥10 푘푔 (1,602푥10−19)2 퐻 6,022푥1023 9 퐹퐸 = 8,988푥10 2 −27 2 1 −11 (1,67푥10 ) 퐹퐺 = 6,674푥10 2 −28 1 퐹퐸 = 2,307푥10 푁 −64 퐹퐺 = (−)1,87푥10 푁 • Electric field, intensity of the electric field (E)
An electric field is a vector field surrounding an electric charge that exerts force on other charges, attracting or repelling them.
Ԧ 1 푄 퐹 = 푞퐸 퐸 = 4휋휀 푟2 퐸 = 1푁퐶−1 = 1푉푚−1 (푆 = 4휋푟2) Gauss’ law – electric flux ΦE The net electric flux through any hypothetical closed surface is equal to 1/ε times the net electric charge within that closed surface. Electric flux is the measure of the distribution of the electric field through a given surface, although an electric field in itself cannot flow. It is one way of describing the electric field strength at any distance from the charge causing the field. Carl Friedrich Gauss (1777–1855) 푞 Φ = Φ = 퐸 푆Ԧ = 퐸푆 푐표푠휃 퐸 휀 퐸
퐸 = 푐표푛푠푡. (electric field) sphere 푆 = 4휋푟2 cylinder 푆 = 2휋푟2푙
푞 푞 = 퐸 4휋푟2 = 퐸 4휋푟2l 휀 휀 1 푞 1 푞 퐸 = 퐸 = 4휋휀 푟2 2휋휀 푟2푙 Shell theorem 1 푞 퐸 = 푟 > 푟 4휋휀 푟2 푠푝ℎ푒푟푒
퐸 = 0 푟 < 푟푠푝ℎ푒푟푒
푑푈 = −퐸푑푟
1 푞 푈 = 푟 > 푟 4휋휀 푟 푠푝ℎ푒푟푒
1 푞 푈푟푠푝ℎ푒푟푒 = 푟 ≤ 푟푠푝ℎ푒푟푒 4휋휀 푟푠푝ℎ푒푟푒 theorem 1: a uniform spherical shell of charge behaves, for external points, as if all its charge were concentrated at its center. theorem 2: a uniform spherical shell of charge exerts no force on a charged particle placed inside the shell. Electric dipole moment – measure of the separation of the electrical charge, measure of the system’s polarity.
Orientation - in chemistry: from positive to negative, in physics: from negative to positive.
-q q 휇 = 푞푟 r - + SI 휇 = 1 퐶푚
1퐷 푑푒푏푦푒 = 3.336푥10−30퐶푚
휇Ԧ = 푞𝑖푟𝑖 𝑖 Permanent dipole
μ=0.0 D μ=1.8546 D
Consequences: high boiling point
Liquid/molar mass Molar mass Dipole Boiling (g/mol) [g/mol] moment*[D point [ oC] ] water ~100 18 1,85 methanol ~64 32 1,70 ethanol ~78 46 1,66 1-propanol ~97 60 1,55 Carbon dioxide -78.5 44 0 (sublimation)
* - gas phase dipole moments • Work and potential energy of the charge in electric field, electric potential
퐸푝표푡 푊 = 퐹푒푥푡ℎ
h 퐹푒푥푡 퐹푔 푊 = ∆퐸푝표푡
푏 + -
1 푾풆풍 > ퟎ 푾풆풍 < ퟎ 2 퐸 푎 + - Work and potential energy (W,E) of the charge (q) in electric field (E), electric potential 흋
An electric potential is the amount of work needed to move a unit positive charge from a reference point to a specific point inside the field without producing any acceleration. φ – electric potential (scalar) 푈 = [휑] = 1 푉 = 1퐽퐶−1
푑푊 퐹푒푥푡푑푟Ԧ U=1V q=1e=1,602x10−19V 푑휑 = = 푞 푞 −19 −퐸푞푑푟Ԧ 퐸(푒푛푒푟푔푦, 푤표푟푘) = 1,602푥10 퐽 = 1푒푉 푑휑 = = −퐸. 푑푟Ԧ 푞 푟푏 푟푏 푑푊 = 푞푑휑 1 푄 ∆휑 = − න 퐸푑푟Ԧ = − න 푑푟 4휋휀 푟2 푊 = 푞푈 푟푎 푟푎 푄 1 1 − = 휑 −휑 = 푈 푊 푞푈 4휋휀 푟 푟 푏 푎 푃 = = = 푈퐼 = 퐼2푅 푏 푎 푡 푡 Dielectrics in electric field
Conductor 퐸푒푥푡 ≠ 0 ------+++++++++++++++++++ 퐸푒푓푓 = 0 + - + - + - + - + + + - 퐸 = 0 - 퐸 + (−)퐸 = 퐸 + - - 푒푥푡 - 𝑖푛푑 + 𝑖푛푑 푒푥푡 + + - + - - - + 퐸 = 0 - + + 𝑖푛푑 - + + - - + - + + + - - + + - - + - + - +
+ - + 퐸푒푥푡
------
+
-
+ -
Dielectric +++++++++++++++++++ 퐸푒푥푡 ≠ 0
+
-
+ -
퐸𝑖푛푑 ≠ 퐸푒푥푡
+
- +
퐸푒푥푡 = 0 - 퐸𝑖푛푑 < 퐸푒푥푡
+
-
+ - 퐸𝑖푛푑 = 0
퐸푒푓푓 = 퐸푒푥푡 − 퐸𝑖푛푑
+
-
+ - 0 휀 휀 0 휀 = 휎 푟 휀 푟 휀
------= =
휀
+ + + + + + + +
휎
+ +
------= 푒푓푓 퐸 ൘
푒푓푓
+ + + + + + + + + +
퐸
------푒푥푡 - 퐸 +++++++++++++++++++ 푒푥푡 퐸
------0 0 푞 휀 휎 휀 푆 푞 = = = 푆 휎 푒푥푡 푒푥푡 퐸 퐸 +++++++++++++++++++ Dielectrics in electric field
1. Electronic polarization, nucleus –electron cloud deformation
2. Atomic polarization- change of the shape of polar molecules
E + - + = + -
3. Orientation polarization- change of the orientation of polar molecules
+ - + - E - + - + - + = + - + - + + - Conductors, semiconductors, insulators (metal, solution of ions)
Superconductors –zero resistance – alloys or compounds, low temperature Semiconductors N-type P-type
resistivity conductivity Insulators ρ Ω푚 σ 푆푚−1 Diamond ~1푥10 12 ~1푥10 −13 insulator Graphite ∥ 2,5푥10−6 2푥105 푏푎푠푎푙 푝푙푎푛푒 − 5,0푥10−6 − 3푥105 conductor Graphite ⊥ 3푥10−3 3,3푥102 푏푎푠푎푙 푝푙푎푛푒 DC circuit - source A voltaic pile, the first battery. It consisted of copper and zinc plates, separated with brine-soaked paper discs
Daniell cell
Open-circuit voltage
U= 1,1018V Electromotive force EMF is the energy transferred per unit charge when one or other type energy is converted into electrical energy.
푊 1퐽 휉 = 휉 = = 1푉 푄 1퐶
푈 = 휉 − 퐼푅
Ideal seat of emf – independent on the U = 휉 − IR R current, internal resistance is zero. 푈
Real seat of emf – potential depends on the current. Resistor R, resistance
U0
U U1
U2 Ohm’s law - the current through a conductor between two points is directly proportional to the
voltage across the two points.
- +
푈 I 퐼 = 푈 = 퐼푅 푅 A 1푉 a ? b 푅 = = 1Ω 1퐴 Georg Simon V Ohm (1789– 1854) Cylindrical conductor (wire) of length l, cross-section S 푙 푅 = 휌 휌 = 1Ω푚 푆 ρ – resistivity, material constant
Electrical conductance – G 푆 1 퐺 = 1ൗ = 휅 퐺 = = 1푆 푠𝑖푒푚푒푛푠 푅 푙 Ω 1 1 Conductivity 휅 = 휅 = = 푆푚−1 휌 Ω푚 Resistors in Series and Parallel 푈 = 푈1 + 푈2 + ⋯ 퐼푅 = 퐼푅1 + 퐼푅2+... 푅 = 푅1 + 푅2+...
푅 = 푅 U 𝑖 𝑖
퐼 = 퐼1 + 퐼2 + 퐼3
I 푈 푈 푈 푈 = + + 푅 푅1 푅2 푅3
U R1 R2 R3 1 1 1 1 U U = + + 푅 푅1 푅2 푅3 I3 I I 1 2 1 1 = 푅 푅𝑖 𝑖 Variation of resistance with temperature – metals
푅 = 푅0 1 + 훼Δ푇
휌 = 휌0(1 + 훼Δ푇)
Semiconductors
퐵 푅 = 퐴푒푇 Capacitors (farad F, μF, pF) 푄 퐶 퐶 = 퐶 = 퐹 = 푈 푉 푄 퐸푆 = (Gauss’ law) 휀
푈 푄 푆 푑푈 = 퐸 푑푟Ԧ 푈 = 퐸푑 푆 = 푄 = 휀 푈 푑 휀 푑
푄0 = 퐶0푈 푄 = 퐶푈 푄 = 퐶0휀푟푈
푆 푆 퐶 = 휀 휀 푄 = 휀 휀 푈 푟 0 푑 푟 0 푑
푑푈 푑퐸 = 퐸푞푑푟Ԧ = 푞 푑푟Ԧ 푝표푡 푑푟Ԧ
푑퐸푝표푡 = 푑푈 푞 = 퐶푈 푑푈 1 퐸 = 퐶푈2 푝표푡 2 Capacitors in Series and Parallel 푄 푈 = 퐶 푈 = 푈1 + 푈2 푈1 = 푈2 = 푈 푄1 = 푄2 = 푄 푄 = 푄1 + 푄2 푄 푄 푄 = + 퐶푈 = 퐶1푈 + 퐶2푈 퐶 퐶1 퐶2 1 1 = σ 퐶 = σ 퐶𝑖 퐶 퐶𝑖
푈1 푈2
푈
푈 푀푒퐴 ⇋ 푀푒푧+ + 퐴푧− 푀푒푧+ + 푧푒− ⟶ 푀푒0 퐴푧− ⟶ 퐴0 + 푧 푒−
2+ − 푍푛퐶푙2 → 푍푛 + 2퐶푙
푍푛2+ + 2푒− → 푍푛0 − − 2퐶푙 → 퐶푙2 + 2푒 Faraday’s I. laws of electrolysis
The mass of the substance (m) deposited or liberated at any electrode is directly proportional to the quantity of electricity or charge (q) passed. 풎 = 푨 푰 풕 푞 = 퐼 푡
풎 = 푨 풒 Michael Faraday (1791-1867)
Faraday’s II. laws of electrolysis
The mass of substances liberated or dissolved by the same amount of electricity is directly proportional to their equivalent masses or equivalent weights .
푚 푛푀 퐴 = = 푞 푛 푧 퐹
푴 푨 = 풛 푭
푧 − 푡ℎ푒 푣푎푙푒푛푐푦 푛푢푚푏푒푟 표푓 𝑖표푛푠, 푛푢푚푏푒푟 표푓 푒푙푒푐푡푟표푛푠 푡푟푎푛푓푒푟푒푑 푝푒푟 𝑖표푛
퐹 − 푡ℎ푒 퐹푎푟푎푑푎푦 푐표푛푠푡푎푛푡, 푡ℎ푒 푐ℎ푎푟푔푒 표푓 1 푚표푙 표푓 푒푙푒푐푡푟표푛푠 …
23 −1 −19 퐹 = 푁퐴푞푒 = 6,022. 10 푚표푙 푥 1,6023. 10 퐶 퐹 = 96486,7 퐶푚표푙−1 Summary
1 푞 푞 Force 퐹 = 1 2 4휋휀 푟2 1 푞 Electric field 퐸 = 4휋휀 푟2 푞 1 Electric potential 휑푎 = 4휋휀 푟푎 Work 푊 = 푞푈 푊 푞푈 Power 푃 = = = 푈퐼 = 퐼2푅 푡 푡 푈 1 1 Resistors 퐼 = serial 푅 = σ𝑖 푅𝑖 푝푎푟푎푙푙푒푙 = σ𝑖 푅 푅 푅𝑖 푅 = 푅0 1 + 훼Δ푇
푆 1 1 Capacitors 퐶 = 휀푟휀0 푄 = 퐶푈 serial = σ parallel 푑 퐶 퐶𝑖 퐶 = σ 퐶𝑖 M Faraday′s laws m = A I t A = z F