J. Velkovska1 Lecture 17: Magnetic field sources. Ampere’s law PHYS 117B.02, Feb-15-08

J. Velkovska 2 Analogies between the electric and magnetic fields on the axis of the dipole For highly symmetric configurations: easy way to get E is from Gauss’s Law ??? Principle of superposition+ Coulomb’s law or Biot-Savart’s law: always works, but may require complicated integrals Ampere’s law

J. Velkovska 3 Line integrals: evaluating the magnetic field along the line

J. Velkovska 4 Easy configurations to evaluate line integrals A straight wire should be easy

J. Velkovska 5 We found B using Biot-Savart’s law already. Now, let’s do it (on the blackboard) using Ampere’s law Outside the wire Inside the wire

J. Velkovska 6 Magnetic Field Lines for a magnetic dipole Magnetic field lines go N->S Use right hand rule to determine the direction of the field from the direction of the current Doesn’t have enough symmetry to use Ampere’s law

J. Velkovska 7 What happens if we add more loops ? The magnetic field of a solenoid

J. Velkovska 8 Some magnets in real life: the PHENIX magnets bend particle trajectory to provide momentum measurement The Central Magnet is 9 meters tall and weighs nearly 500 tons. The Int(B.dl) at 90 degrees is 0.78 Tesla-meters.

J. Velkovska 9 The PHENIX experiment magnet coils One of the central magnet coils under A LOT of steel The coils before installation

J. Velkovska 10 The solenoidal magnet of the STAR detector

J. Velkovska 11 The particle tracks: Au+Au colliding head on at 200 GeV in c.m. system or in p+p collisions UA1, 900 GeV

J. Velkovska 12 The Relativistic Heavy Ion Collider 2 counter-circulating rings  2.4 miles circumference  1740 super conducting magnets Collides any nucleus on any other Top energies: 200 GeV Au-Au 500 GeV polarized p-p Four experiments:BRAHMS, PHOBOS PHENIX, STAR

J. Velkovska 13 The Large Hadron Collider 27 km circumference tunnel 3.8 m. in diameter, buried 50 to 175 m below ground straddles the French-Swiss border to the North-West of Geneva 1232 dipole magnets bend the beam Top energy: 14 TeV for pp, 5.5 TeV PbPb 4 detectors : ALICE, CMS, ATLAS, LHCb

J. Velkovska 14 Some pictures from the LHC A magnet going down the shaft. Inside the tunnel. The LHC start-up is in summer 2008 !

J. Velkovska 15 The CMS detector: Vanderbilt is involved both in HE and HI side