Sources of Magnetic Fields Sources of Magnetic Fields Chapter 28 - - PowerPoint PPT Presentation

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Sources of Magnetic Fields Sources of Magnetic Fields Chapter 28 - - PowerPoint PPT Presentation

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Sources of Magnetic Fields Sources of Magnetic Fields Chapter 28 October 25, 2012 Physics 208 1 Learning Goals.. The nature of the magnetic field produced by a moving charge. How to describe the magnetic field produced by an element of

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Sources of Magnetic Fields Sources of Magnetic Fields

Chapter 28

October 25, 2012 Physics 208 1

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Learning Goals..

  • The nature of the magnetic field produced by a moving charge.
  • How to describe the magnetic field produced by an element of a

current carrying conductor current carrying conductor.

  • How to calculate the magnetic field of a long straight current

carrying wire. Why wires carrying current in the same direction attract and

  • Why wires carrying current in the same direction attract and

carrying current in opposite directions repel.

  • How to calculate the magnetic field for current carrying wires

bent in a circle bent in a circle.

  • What is Ampere’s Law and what does it tell us about magnetic

fields. H t A ’ L t l l t ti fi ld f

October 25, 2012 Physics 208 2

  • How to use Ampere’s Law to calculate magnetic fields for

symmetric current distributions.

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Magnetic field produced by a moving charge

charge moving a for field magnetic The point source the from pointing vector a is where ˆ 4 charge moving a for field magnetic The

2

r r r v q B r r r × = π μ

October 25, 2012 Physics 208 3

point. field the to point source the from pointing vector a is where r

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Magnetic field produced by a moving charge

charge moving a for field magnetic The

2

ˆ 4 c a ge

  • v g

a

  • e d

ag et c e r r v q B × = π μ r r With point. field the to point source the from pointing vector a is where r r

2 2 7

/ s N 10 4 C

−

× = π μ

October 25, 2012 Physics 208 4

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October 25, 2012 Physics 208 5

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Force between parallel wires

H Bi t d S t d th i How Biot and Savart made their measurements on magnetic forces using parallel wires.

October 25 2012 Physics 208 6

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Now let’s find the field for a circular loop

  • f

i e ith a adi s R

  • f wire with a radius R..

October 25, 2012 Physics 208 7

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October 25, 2012 Physics 208 8

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October 25, 2012 Physics 208 9

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Ampere’s law….. p (finding B-fields using symmetry

October 25, 2012 Physics 208 10

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October 25, 2012 Physics 208 12

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Path without necessary symmetry symmetry Good Path

October 25, 2012 Physics 208 13

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The Solenoid…

October 25, 2012 Physics 208 15

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The CDF Detector and Solenoid

October 25, 2012 Physics 208 16

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An event

display display from the CDF CDF Detector

October 25, 2012 Physics 208 17

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The CMS magnet being lowered into place at the LHC p

October 25, 2012 Physics 208 18

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Using Ampere’s Law..

October 25, 2012 Physics 208 19

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Solving for B….

October 25, 2012 Physics 208 20

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The Toroid….

October 25, 2012 Physics 208 21

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The MINOS Detector and Toroid

October 25, 2012 Physics 208 22

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Example of a charged particle’s trajectory in MINOS

October 25, 2012 Physics 208 23

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The Atlas Experiment at the LHC

October 25, 2012 Physics 208 24

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Current configurations with enough Current configurations with enough symmetry to use Ampere’s Law…….

Infinite cylinder Infinite planes of wires

  • r sheets of current

Infinitely long cylindrical shells

October 25, 2012 Physics 208 26

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Choosing the right Amperian Loop to integrate around for these current configurations….. configurations….. Need to find paths that have either B = 0 or B fixed to use Ampere’s Law to solve for B.

October 25, 2012 Physics 208 27