Physics54S09II

Physics54S09II - Ch 28: Sources of the Magnetic Field L12...

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Unformatted text preview: Ch 28: Sources of the Magnetic Field L12 Memorize this! Focus: Amperes Law, Line Integral of B Amperes Law (1775-1836) I d = l B ANY Loop Current INSIDE Loop B ? I B Right Hand Rule! RH Screw along I Amperes Law always true, but useful for finding B if there is Symmetry Line integral of B is zero. I out I in Equal currents in/out B l d B B l d Ch 28: Sources of the Magnetic Field L12 I d = l B Example : B-Field outside long wire. r I B Direction of B ? Direction of d l ? d l Does B change magnitude around loop ? wire for 2 ) ( ) ( 2 R r r I r B I r rB > = = What is B if we look inside the wire exactly at the center ? m/A T 10 4 7 = Ch 28: Sources of the Magnetic Field L12 How do we find B 3 at wire 3? Loop around both 1 and 2 or 1 and 2 separately? Use superposition and symmetry : Symmetry for wire 1: 2 r 1 B 1 = I 1 Symmetry for wire 2: 2 r 2 B 2 = I 2 RHR: B 1 at wire 3 into page B 2 at wire 3 out of page Example: Force per unit length on wire 3? I 3 = 1 A I 1 = 2 A I 2 = 2 A 2 m 0.25 m B 3 B 3 = B 2 B 1 Net B 3 out of page (why?) Force on wire 3 is F 3 = I 3 B 3 L 3 so force per unit length is F 3 / L 3 = I 3 B 3 What is r 1 ? RHR: Force away from the upper two wires (why?) What is r 2 ? I d = l B Ch 28: Sources of the Magnetic Field L13 B out = 0 Example : Field of a long Solenoid + + + = 4 3 2 1 l B l B l B l B l B d d d d d 1 2 4 3 = 0 = 0 Why? = B l Why? Fields of upper and lower wires? l B in N turns in length l , current I NI I Bl d = = = total l B I n B = l N n / = number of turns / unit length I d = l B Flux of B : Gausss Law in Magnetism = a E Q d Electric Charge Surface bounding volume Q = charge in volume = a B d No Magnetic Charges Exist! Any closed surface Magnetic flux in = magnetic flux out: Lines never begin anywhere, just close. Ch 28: Sources of the Magnetic Field L13 Focus: Time-varying B induces E Sign = Lenzs law : Induced voltage and current tries to generate a magnetic field which opposes change in magnetic flux . Ch 29: Electromagnetic Induction and Faradays Law L14 B I(t) N turns ) ( t Time-varying B Time-varying voltage (EMF) Memorize! Faradays Experiment * EMF induced in Blue Loop dt d B t = ) ( Faradays Law Rate of change of total magnetic flux B in Blue Loop Ch 29: Electromagnetic Induction and Faradays Law L14 Magnetic Flux = Field times area: Unit = m 2 Tesla = Weber lux in Magnetism A B If B is uniform : cos AB B = = A B = a B d B In general: 2 3 2 1 Example: Find the total flux for two right triangles of wire: Which way should the area vectors point? Out of the page or in, both the same or different?...
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This note was uploaded on 05/13/2010 for the course PHYSICS 54L taught by Professor Thomas during the Spring '09 term at Duke.

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Physics54S09II - Ch 28: Sources of the Magnetic Field L12...

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