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A New Topic: Magnetic Fields P14 - 1

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Chapter 28 and 29 Hour 1: General introduction, Gauss Law Magnetic force (28.1) Cross product of vectors. Hour 2: Currents create B Fields: Biot-Savart, B field of loops (magnetic moment). (28.2) Hour 3: Use Amperes Law to calculate B fields (28.3) Hour 4: Charged particles motion in B field. (29.1) Hour 5: B field force & torque on wires with I (29.2) Hour 6: Magnetic materials (29.4)

Slide 3

Gravitational Electric Fields Mass mCharge q () r2r2 m m g Gr er 2er 2 rr q E kE k Create: FE qEFE qE Fg mgFg mg Feel: Also saw Create: Dipole p p E p E Feel: P14 - 3

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Magnetism Bar Magnet Like poles repel, opposite poles attract P14 - 4

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Magnetic Field of Bar Magnet (1)A magnet has two poles, North (N) and South (S) (2)Magnetic field lines leave from N, enter at S P14 -

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Bar Magnets Are Dipoles! Create Dipole Field Rotate to orient with Field Is there magnetic mass or magnetic charge? NO!Magnetic monopoles do not exist in isolation P14 - 6

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Magnetic Monopoles? Magnetic Dipole -qq When cut: 2 monopoles (charges) p Electric Dipole When cut:2 dipoles Magnetic monopoles do not exist in isolation Another Maxwells Equation! (2 of 4) Gausss Law Magnetic Gausss Law P14 - 7

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Fields: Grav., Electric, Magnetic Mass mCharge q () r2r2 m m g Gr er 2er 2 rr q E kE k No Magnetic Monopoles ! Create: FE qEFE qE Fg mgFg mg Feel: Also saw Create: p E p E Dipole p E P14 - 8 Dipole m Feel: m B m B B B

Slide 9

What else is magnetic? P14 - 9

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Magnetic Field of the Earth Also a magnetic dipole! P14 - 10 North magnetic pole located in southern hemisphere

Slide 11

Visualization: Bar Magnet & Earths Magnetic Field (http://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/magnetostatics/27-barmagontable/27- barmag320.html)http://ocw.mit.edu/ans7870/8/8.02T/f04/visualizations/magnetostatics/27-barmagontable/27- barmag320.html) P14 - 11

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MagneticFieldBThusFar Bar Magnets (Magnetic Dipoles) Create: Dipole Field Feel: Orient with Field Does anything else create or feel a magnetic field? P14 - 12

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Moving Charges Feel Magnetic Force FBq v BFBq v B Magnetic force perpendicular both to: Velocity v of charge and magnetic field B P14 - 13

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MagneticFieldB:Units FBq v BFBq v B Since coulomb meter/second P14 - 14 C m sA mC m sA m B Units newton 1 N 1 N This is called 1 Tesla (T) 1T=1041T=104 Gauss(G)

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Recall: Cross Product P14 - 15

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Notation Demonstration P14 - 16 OUT of page Arrow Head INTO page Arrow Tail XXXX XXXX XXXX XXXX

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Cross Product: Magnitude Computing magnitude of cross product A x B: C AB sin C AxBC AxB |C |:|C |: P14 - 17 area of parallelogram

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Cross Product: Direc tion Right Hand Rule #1: 1)Curl fingers of right hand in the direction that moves A (green vector) to B (red vector) through the smallest angle 2)Thumb of right hand will point in direction of the cross product C (orange vector) C AxBC AxB http://ocw.mit.edu/ans7870/8/8.02T/f04/visualizat ions/vectorfields/14-CrossProduct/14- crossprod320.html P14 - 18

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Cross Product: Signs P14 - 19 j i kk j ii k jj i kk j ii k j i j kj k ik i ji j kj k ik i j Cross Product is Cyclic (left column) Reversing A & B changes sign (right column)

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PRS Questions: Right Hand Rule P14 - 20

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Putting it Together:Lorentz Force F q E v BF q E v B This is the final word on the force on a charge P14 - 21 FBq v BFBq v B C harges Fee l F E qE Electric Fields Magnetic Fields

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Application: Velocity Selector What happens here? P14 - 22

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Velocity Selector Particle moves in a straight line when q(E v B) 0 v q(E v B) 0 v P14 - 23 FnetFnet E B

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PRS Question: Hall Effect P14 - 24