How do electromagnetic lenses focus an electron beam in an electron microscope?

In an electron microscope, electromagnetic lenses focus an electron beam by utilizing the Lorentz force, which acts on charged particles moving through a magnetic field.12

Modern electromagnetic lenses consist of a solenoid of wire combined with a magnetic pole piece that creates and concentrates a strong magnetic field. As electrons pass through this field, they experience a force perpendicular to both their velocity and the magnetic field lines. This force causes the electrons to follow a curved trajectory, effectively converging the beam toward a focal point.12

Unlike optical lenses, which have a fixed focus, electromagnetic lenses are variable-focus; the magnification and focus of the microscope are adjusted by precisely controlling the electrical current flowing through the lens coils. Because these lenses are always convergent, they cannot be corrected for spherical aberration using a second lens of opposite characteristics, which remains a fundamental limiting factor in the instrument's resolving power.1