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The magnetic field inside an ideal solenoid cavity with an arbitrarycross-section is always constant, while it is always zero outside the solenoid.We can make a solenoid lens that can focus a parallel beam to a point behind itby adjusting the curvature of the solenoid circumference. In this paper, wediscuss the design of magnetic lenses ranging from simple geometries to thegeneral ones. We discovered that there are an infinite number of curvaturesthat can be used to focus the parallel beam to a specific focal point. Usingthis property, we also present the concept of a simple mass spectrometer bymeasuring the intensity of the ion captured by a detector placed at the focalpoint. This result is expected to enrich learning material in undergraduatecourses, especially for the topic of electricity and magnetism.

Magnetic Lens Made of a Single Solenoid for Controlling Bending of Two-Dimensional Ion Beam