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L10_Viet_Potential and Potential Energy

# L10_Viet_Potential and Potential Energy - Physics 122...

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Physics 122 Electricity and Magnetism Lecture 10 Potential and Potential Energy

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05/07/09 Physics 122 - Lecture 10 2 Kirchhoff’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
05/07/09 Physics 122 - 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 E -field 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

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05/07/09 Physics 122 - Lecture 10 4 Resistivity and Conducting Materials For many applications, it is more convenient to use inverse of conductivity, which is called the resistivity , 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 = = Nm 2 /CA = Nm 2 s/C 2 ρ = σ = Units of resistivity are m
05/07/09 Physics 122 - Lecture 10 5 Example : The Electric Field in a Wire 2 7 -1 -1 2 (0.80 A) 0.0072 N/C (3.5 10 m ) (.0010 m) J I I E A r σ σ σπ π = = = = = 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?

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05/07/09 Physics 122 - Lecture 10 6 Resistors 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 resistor , a circuit element characterized by an electrical resistance 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 ( ) . Multiple resistors may be combined in series , where resistances add, or in parallel , where inverse resistances add.
05/07/09 Physics 122 - Lecture 10 7 Superconductivity The “classical” physics we are studying is an approximation to quantum mechanics. In the quantum

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L10_Viet_Potential and Potential Energy - Physics 122...

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