C29 - Magnetic Fields

magnetic force

• B = magnetic field vector

Lorentz force

the combination of magnetic and electric forces

magnetic force rules

• proportional to velocity

• proportional to sinθ

  • 0 when moving || mag. lines

  • max. when moving ⟂ mag. lines

• - & + particles are forced opposite ways

• F_B points ⟂ both v & B (x product)

right-hand rules

magnetic force units

tesla (T = N/(A • m) = N/(C • m/s)))

circular motion in uniform magnetic field

• r = mv/qB

• ω = qB/m

  • cyclotron frequency

• T = 2πm/qB

velocity selector

combination of F_e in one direction & F_B in the other, allows for only specific velocities of particles to pass (& in a straight line)

• v = E/B

mass spectrometer

separates ions based on mass-charge ratio along circular path

• based on fixed velocity (from velocity selector)

cyclotron

first successful particle accelerator

• alternating current + magnetic field moves particles in an increasingly larger & faster circular path by constantly swapping voltage

energy (particles exiting cyclotron)

(qBR)²/2m

magnetic force (on a current-carrying wire segment; uniform electric & magnetic fields)

torque (on a current loop; uniform field)

magnetic dipole moment

potential energy (current loop in a magnetic field)

Hall effect

an electrical potential difference between the top and bottom of a current-carrying segment, induced by a magnetic field

Hall voltage

R_H = 1/nq = Hall coeff.