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

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 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. How to use Ampere’s Law to calculate magnetic fields for H t A ’ L t l l t ti fi ld f � symmetric current distributions. October 25, 2012 Physics 208 2

Magnetic field produced by a moving charge The The magnetic magnetic field field for for a a moving moving charge charge r r μ × ˆ q v r = 0 B π 2 4 r r where where is is a a vector vector pointing pointing from from the the source source point point r r to the field point. October 25, 2012 Physics 208 3

Magnetic field produced by a moving charge The e magnetic ag et c field e d for o a a moving ov g c a ge charge r r μ × ˆ q v r = 0 B π 2 4 r r where is a vector pointing from the source point r to the field point. With μ = π × − 7 2 2 4 10 N s / C 0 October 25, 2012 Physics 208 4

5 Physics 208 October 25, 2012

Force between parallel wires H How Biot and Savart made their Bi t d S t d th i measurements on magnetic forces using parallel wires. October 25 2012 Physics 208 6

Now let’s find the field for a circular loop of of wire with a radius R.. i e ith a adi s R October 25, 2012 Physics 208 7

8 Physics 208 October 25, 2012

9 Physics 208 October 25, 2012

Ampere’s law….. p (finding B-fields using symmetry October 25, 2012 Physics 208 10

11 Physics 208 October 25, 2012

12 Physics 208 October 25, 2012

Path without necessary symmetry symmetry Good Path October 25, 2012 Physics 208 13

14 Physics 208 October 25, 2012

The Solenoid… October 25, 2012 Physics 208 15

The CDF Detector and Solenoid October 25, 2012 Physics 208 16

� An event display display from the CDF CDF Detector October 25, 2012 Physics 208 17

The CMS magnet being lowered into place at the LHC p October 25, 2012 Physics 208 18

Using Ampere’s Law.. October 25, 2012 Physics 208 19

Solving for B…. October 25, 2012 Physics 208 20

The Toroid…. October 25, 2012 Physics 208 21

The MINOS Detector and Toroid October 25, 2012 Physics 208 22

Example of a charged particle’s trajectory in MINOS October 25, 2012 Physics 208 23

The Atlas Experiment at the LHC October 25, 2012 Physics 208 24

25 Physics 208 October 25, 2012

Current configurations with enough Current configurations with enough symmetry to use Ampere’s Law……. Infinite cylinder Infinite planes of wires or sheets of current Infinitely long cylindrical shells October 25, 2012 Physics 208 26

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