Chapter 21 Magnetic Force

Clicker A)1.7 V B)3.4 V C)5.1 V D)6.8 V E)12 V What is the potential difference across the clams when I take bulb out of circuit?

The Biot-Savart law for a moving charge The Biot-Savart law for a short piece of wire: How magnetic field affects other charges? Magnetic Field of a Moving Charge

Direction of the magnetic force depends on: the direction of B the direction of v of the moving charge the sign of the moving charge q – charge of the particle v – speed of the particle B – magnetic field Magnetic Force on a Moving Charge

A negative charge is placed at rest in a magnetic field as shown below. What is the direction of the magnetic force on the charge? A.Up B.Down C.Into the page D.Out of the page E.No force at all. B

A.Up B.Down C.Into the page D.Out of the page E.No force at all. A negatively charged particle is moving horizontally to the right in a uniform magnetic field that is pointing in the same direction as the velocity. What is the direction of the magnetic force on the charge? B V

A.Left B.Up C.Down D.Into the page E.Out of the page Now, another negatively charged particle is moving upward and to the right in a uniform magnetic field that points in the horizontal direction. What is the direction of the magnetic force on the charge? V B

Current: many charges are moving Superposition: add up forces on individual charges Number of moving charges in short wire: Total force: I Force of a short wire: In metals: charges q are negative. Will this equation still work? Magnetic Force on a Current-carrying Wire

Ampere is defined as a current at which two very long parallel wires 1 m apart create a force on each other of N per meter length. From this also follows that  0 /(4  ) = T. m/A Forces Between Parallel Wires Definition of 1 Ampere:

For long wire: Magnetic force on lower wire: Magnetic force on upper wire: What if current runs in opposite directions? Forces Between Parallel Wires Electric forces: “likes repel, unlikes attract” Magnetic forces: “likes attract, unlikes repel”

What is the effect on the magnitude of speed? Kinetic energy does not change Magnetic field cannot change a particle’s energy! Magnetic field cannot change a particle’s speed! Magnetic force can only change the direction of velocity but not its magnitude Effect of B on the Speed of the Charge

Single electron in television tube: (v<<c) e/m e = C/kg Magnitude of the Magnetic Force

Any rotating vector: Circular Motion at any Speed  …angular speed Cyclotron Frequency

if v<<c: Alternative derivation: Circular motion: Period T: Circular Motion at Low Speed independent of v! Non-Relativistic

v<<c :  V equivalent ~ 10 8 V  v~c : need to adjust B or  A Cyclotron

What if v is not perpendicular to B? Direction? Magnitude? Trajectory: helix Exercise

Determining e/m of an Electron

1897: m/e >1000 times smaller than H atom Joseph John Thomson ( )

Magnetic force can only change the direction of velocity but not its magnitude (high q – small R, large m large R) Applications: find p, e/m, separate particles (including 238 U and 235 U (natural abundance 0.7%) isotopes

Proton energy Velocity, m/sec R, m 1MeV1.3* m 7000 GeV e = 1.6* C m proton = 1.7* kg Giga 10 9 What is the radius of circle of proton accelerated over 7000GeV in B =5.5 T? Proton energy Velocity, m/sec R, m 1MeV1.3* m 7000 GeV c4.2 km Proton speed up to c

Fermilab: Tevatron CERN: Large Hadron Collider To keep R constant B is increased up to 3 T (superconducting coils) Particle Accelerator Applications: study nucleus – accelerate particles (protons) and shoot at nucleus to observe nuclear reactions create new particles by colliding particles Synchrotron – source of synchrotron radiation

Argonne National Laboratory