J. Velkovska 1

Lecture 17: Magnetic field sources. Ampere’s law

PHYS 117B.02 , Feb-15-08

J. Velkovska 2

Analogies between the electric and magnetic fields

03

24loop

IAB

z

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 lawOutside 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