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Unformatted text preview: Physics 2212 Electricity and Magnetism Lectur e 10 (Knight: 29.1 to 29.4) Potential and Potential Ener gy 10/06/09 Physics 2212  Lecture 10 2 Kir chhoff’s Junction Law in out I I = ∑ ∑ 0; summed over all the currents to any "junction". i i I = ∑ The current density is generally not the same at all points of the wire 10/06/09 Physics 2212  Lecture 10 3 Conductivity and Resistivity 2 d e E ne J nev ne E m m τ τ = = = 2 conductivity: so ne J E m τ σ σ ≡ = The current density J = nev d is directly proportional to the electron drift speed v d . Our microscopic conduction model gives v d = e τ E/m , where τ is the mean time between collisions. Therefore: The quantity ne 2 τ /m depends only on the properties of the conducting material, and is independent of how much current density J is flowing. This suggests a definition: This result is fundamental and tells us three things: (1) Current is caused by an Efield exerting forces on charge carriers; (2) Current density J and current I=JA depends linearly on E ; (3) Current density J also depends linearly on σ . Different materials have different σ values because n and τ vary with material type. J = σ E 10/06/09 Physics 2212  Lecture 10 4 Resistivity and Conducting Mater ials For many applications, it is more convenient to use inverse of conductivity, which is called the r esistivity , denoted by the symbol ρ : 2 1 resistivity: m ne ρ σ τ ≡ = Thus, the current density is J = E σ = E/ ρ . Here are the conducting properties of common materials: Units: ohms = Ω = Nm 2 /CA = Nm 2 s/C 2 ρ = σ = Units of resistivity are Ω m 10/06/09 Physics 2212  Lecture 10 5 Example : The Electr ic Field in a Wir e 2 711 2 (0.80 A) 0.0072 N/C (3.5 10 m ) (.0010 m) J I I E A r σ σ σπ π = = = = = × Ω The electric field strength is A 2.0 mm diameter aluminum wire carries a current of 800 mA. What is the electric field strength inside the wire? 10/06/09 Physics 2212  Lecture 10 6 Resistor s and Resistance R net 1 2 3 Series Connection [ L]: net R R R R Σ = + + 1 2 3 Parallel Connection [ (1/A)]: 1 1 1 1 net R R R R Σ = + + R net I Conducting material that carries current along its length can form a r esistor , a circuit element characterized by an electr ical r esistance R: R ≡ ρ L/A where L is the length of the conductor and A is its cross sectional area. R has units of ohms ( Ω ) . Multiple resistors may be combined in ser ies , where resistances add, or in par allel , where inverse resistances add. For identical resistors can simply add the lengths For identical resistors can simply add the areas 10/06/09 Physics 2212  Lecture 10 7 Super conductivity The “classical” physics we are studying is an approximation to quantum mechanics. I n the quantum domain, under certain circumstances (low temperature, electron pairing) , there may be minimum amount of energy that an electron can lose in a collision. I f the probable energy loss falls below that minimum, the...
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 Fall '09
 GEIST
 Current, Magnetism, Energy, Potential Energy, Trigraph, Welec, el ectr, ener gy

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