CHARGE PARTICLES
Milikan's experiment

extra high tension pd applied between metal plates > -vely charge oil drop held stationery bet plates
F_up = F_down
qE = ma (m = vol × density)
qV/x = 4πr³ρg/3
q = 4πr³ρgx/3V
Milikan found charges on oil drop equal multiples of 1.6 × 10^-19C (= fundamental unit of charge, assumed as smallest unit)
all data from Milikan's experiment: multiple of 1.6 × 10^-19C, never less

large oil drop can't be used as weight greater than possible upward force
> use tiny oil drops => can't measure radius directly

Finding radius: electric field turned off > terminal velocity found (v = y/t)
by Stoke's Law: retarding F = 6πηrv (η = coefficient of viscousity of air)
weight = viscous F + upthrust (upthrust = 4πr³σg/3, σ = density of air)
since upthrust v.small > negligible > ignored
weight = viscous F
4πr³ρg/3 = 6πηrv = 6πηry/t => r = √(9ηy/2ρgt) => from r, q can be found

Deflection in uniform elec field

electron: attracted towards +ve plate
paraboic path bet plates due to const upward F, F_E = eE
for +ve charge: deflected towatds -ve plates, F_E = qE)
Deflection in uniform magnetic field

deflectn according to Flemmings LH rule
circulr path bet plates due to const perpendicular F, F_B = evB = mv²/r
r = mv/Be

Velocity selection using electric & magnetic field

F_E = eE
F_B = evB

A: F_E > F_B
C: F_E < F_B
B: F_E = F_B => eE = Bve p> v = E/B
can select vel by changin E & B
Determining velocity

assume electron emitted from rest at cathode and accelerated to anode > electron exits anode w/ vel,v
loss in PE = gain in KE
eV = ½mv² => v = √(2eV/m)
Determining e/m_e

F_B = evB = mv²/r => v = eBr/m
v = eBr/m = √ (2eV/m) => e/m = 2V/B²r²

(1) E, B = 0 => no deflectn => note position of spot on screen
(2) apply fixed mag field w/o elec field => deflectn down
(3) elec field adjusted until spot returns to original undeflected position
   F_E = F_B => eE = Bve p> v = E/B
   loss in PE = gain in KE
   eV = ½mv² = ½m(E/B)²
   => e/m = ½E²/B²V

Mass spectrometer
use to -accurately determine m/e ratio, -analyse diff elements / isotopes

+ve ions from same element directed through slits S₁ & S₂
ions emerge w/ diff speeds & charges => use vel selector to obtain particles w/ certain speed which pass thorugh S₃
due to mag field > circular path onto photographic film
F = qvB = mv²/r => r = mv/qB = m/q × E/B²
r ∝ m/q


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