Lecture_22_Part_1

Lecture_22_Part_1 - Chapter 21 Patterns of Fields in Space...

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Chapter 21 Patterns of Fields in Space • Electric flux • Gauss’s law • Ampere’s law • Maxwell equations
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Electrostatic phenomena Magnetic phenomena Coulomb law: r r Q Q F ˆ 4 1 2 2 1 0 !" = r Biot-Savart law: 2 0 ˆ 4 r r v q B ! = r r " μ Magnetic force: B v q F r r r ! = q F E r r = Principle of superposition Electric field: q U V = Potential: x V E x ! ! " = V A ! V B = ! r E " d r l B A # Fundamentals
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What is in the box? no charges? vertical charged plate? Patterns of Fields in Space
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Box versus open surface Seem to be able to tell if there are charges inside …no clue… Gauss’s law: If we know the field distribution on closed surface we can tell what is inside. Patterns of Fields in Space
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Need a way to quantify pattern of electric field on surface: electric flux 1. Direction flux>0 : electric field comes out flux<0 : electric field goes in +1 -1 0 Relate flux to the angle between outward-going normal and E: flux ~ cos( θ ) Electric Flux: Direction of E
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2. Magnitude flux ~ E flux ~ E cos( θ ) flux ~ r E ! ˆ n E cos " = r E ! ˆ n = E ˆ n cos Electric Flux: Magnitude of E
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3. Surface area flux through small area: A n E flux ! " ˆ ~ r Definition of electric flux on a surface: ! " # surface A n E ˆ r Electric Flux: Surface Area
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Perpendicular field ! cos ˆ AE A n E " = " # r ! " = " # AE A n E ˆ r Perpendicular area cos cos ˆ y x E A E A n E " " = " = " # r Δ x Δ y ! " = " # A E A n E ˆ r Electric Flux: Perpendicular Field or Area θ
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! " # surface A n E ˆ r ! " dA n E ˆ r A d r ! " A d E r r ! " = A d E r r surface closed a on flux electric Adding up the Flux
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0 ˆ ! " " = # $ inside surface q A n E r ! " = # 0 ˆ $ inside q dA n E r Proof: 1. Proportionality constant 2. Size and shape independence 3. Independence on number of charges inside 4. Charges outside contribute zero Gauss’s Law
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0 ˆ !
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This note was uploaded on 04/02/2008 for the course PHYS 272 taught by Professor K during the Winter '07 term at Purdue.

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Lecture_22_Part_1 - Chapter 21 Patterns of Fields in Space...

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