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How do magnetic fields focus and deflect electron beams in an electron microscope?

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In an electron microscope, magnetic fields are used to focus and deflect electron beams by exerting a force on the moving electrons, a phenomenon described by the Lorentz force.

The Role of Electromagnetic Lenses

Modern electron microscopes utilize electromagnetic lenses, which consist of a solenoid of wire and a magnetic pole piece designed to create and concentrate a magnetic field. Because electrons are charged particles, they experience a force when moving through these fields. This force is always perpendicular to both the velocity of the electron and the direction of the magnetic field, which allows the lenses to bend the electron paths and bring them to a focus.123

Deflection and Focusing

Deflection: When an electron moves through a magnetic field, the magnetic force acts to deflect the particle's trajectory without changing its speed. If the electron's velocity is perpendicular to the magnetic field, it follows a circular path; if it enters at an angle, it follows a helical path.243
Focusing: By precisely controlling the current through the lens coils, microscopists can adjust the strength of the magnetic field. This allows for variable-focus control, enabling the instrument to focus the electron beam on a specimen or determine the final magnification of the image.1

While these lenses are essential for imaging, they are always convergent and suffer from inherent aberrations, such as spherical aberration, which ultimately limits the microscope's resolving power.1