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How do electric and magnetic fields alter the paths of ions in a mass spectrometer?

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In a mass spectrometer, electric and magnetic fields are used to manipulate the paths of ions to separate them based on their mass-to-charge ratios.1

Electric Fields

Electric fields are primarily used to accelerate ions from the source into the mass analyzer using a system of electrostatic slits. Additionally, in devices like the quadrupole mass spectrometer, superimposed radio-frequency and constant potentials are applied between parallel rods. This creates an electric field that acts as a mass filter, allowing only ions within a specific mass range to maintain stable oscillations and reach the detector.12

Magnetic Fields

When ions move through a magnetic field perpendicular to their direction of travel, they follow a circular path. For a monoenergetic ion beam, the radius of this path depends on the ion's mass-to-charge ratio ( $m / z$ ). The relationship is defined by the equation:3
$\frac{m}{z} = \frac{B^{2} r^{2}}{2 V}$
where $B$ is the magnetic field strength, $r$ is the radius of curvature, and $V$ is the accelerating voltage. By controlling these parameters, the magnetic field effectively separates ions into their various mass components.3