Formula: Mass Spectrometer Mass Electric charge Radius of the circular path Plate distance Voltage Magnetic flux density (B-field)
$$\class{brown}{m} ~=~ \frac{ q \, r \, d \, \class{violet}{B}}{ \class{green}{U} }$$
$$\class{brown}{m} ~=~ \frac{ q \, r \, d \, \class{violet}{B}}{ \class{green}{U} }$$
$$q ~=~ \frac{ \class{brown}{m} \, \class{green}{U}}{r \, d \, \class{violet}{B} }$$
$$r ~=~ \frac{ \class{brown}{m} \, \class{green}{U}}{q \, d \, \class{violet}{B} }$$
$$d ~=~ \frac{ \class{brown}{m} \, \class{green}{U}}{q \, r \, \class{violet}{B} }$$
$$\class{green}{U} ~=~ \frac{ q \, r \, d \, \class{violet}{B}}{ \class{brown}{m} }$$
$$\class{violet}{B} ~=~ \frac{ \class{brown}{m} \, \class{green}{U}}{q \, d \, r }$$
Mass
$$ \class{brown}{m} $$ Unit $$ \mathrm{kg} $$
Mass of the charged particle exiting behind the aperture of the mass spectrometer.
Electric charge
$$ q $$ Unit $$ \mathrm{C} = \mathrm{As} $$
Charge of a particle shot into the mass spectrometer.
Radius of the circular path
$$ r $$ Unit $$ \mathrm{m} $$
Radius of the semicircular orbit of the particle created behind the aperture.
Plate distance
$$ d $$ Unit $$ \mathrm{m} $$
Distance between the two electrodes of the capacitor.
Voltage
$$ \class{green}{U} $$ Unit $$ \mathrm{V} = \frac{ \mathrm J }{ \mathrm C } = \frac{ \mathrm{kg} \, \mathrm{m}^2 }{ \mathrm{A} \, \mathrm{s}^3 } $$
Voltage between the capacitor plates.
Magnetic flux density (B-field)
$$ \class{violet}{B} $$ Unit $$ \mathrm{T} = \frac{\mathrm{kg}}{\mathrm{A} \, \mathrm{s}^2} $$
External magnetic field in which the plate capacitor is placed. This magnetic field is also outside the capacitor behind the aperture. This field is responsible for the charge to perform a circular motion.