22.11 More Applications of Magnetism

Magnetic Field Applications

Mass Spectrometry and Magnetic Fields

A mass spectrometer separates ions by mass using magnetic fields. It's one of the most precise tools for identifying unknown substances and measuring atomic masses.

Here's how the process works:

1. Ionization: An electron beam strips electrons from sample atoms, creating positively charged ions.
2. Acceleration: An electric field accelerates all ions, giving them a uniform kinetic energy.
3. Deflection: The ions enter a region with a uniform magnetic field perpendicular to their velocity. The magnetic force causes each ion to travel in a curved (circular) path.
4. Detection: A detector records where each ion strikes after curving through the field. That position reveals the ion's mass-to-charge ratio.

The key physics: the radius of the curved path depends on the ion's mass-to-charge ratio. Heavier ions (larger $\frac{m}{q}$) curve less and hit the detector farther from the entry point. Lighter ions curve more tightly and land closer.

If you know the charge (most ions are singly charged, so $q = e$), the mass-to-charge ratio gives you the mass directly.

Principles of MRI in Medicine

MRI (Magnetic Resonance Imaging) produces detailed images of soft tissue without surgery or ionizing radiation. It relies on a phenomenon called nuclear magnetic resonance (NMR).

Certain atomic nuclei (those with an odd number of protons or neutrons) have an intrinsic magnetic moment, meaning they behave like tiny magnets. MRI targets hydrogen nuclei (single protons), which are abundant in water and fat throughout the body.

The imaging process works in three stages:

1. Alignment: A strong external magnetic field causes hydrogen protons to align either parallel or antiparallel to the field.
2. Excitation: A pulse of radio waves at a specific frequency flips the protons out of alignment.
3. Relaxation and detection: When the radio pulse stops, the protons relax back to their aligned state and emit radio waves as they do. Detectors pick up these emitted signals.

Signal strength depends on proton density, which varies between tissue types. Dense-proton tissues (like water-rich organs) produce stronger signals than tissues with fewer protons. This difference in signal creates contrast in the image.

To build a full 2D or 3D image, the MRI machine uses gradient magnetic fields that vary slightly across the body. These gradients encode spatial information so the system can map exactly where each signal originates.

Common medical uses include diagnosing tumors, spinal cord injuries, brain abnormalities, and muscle or organ damage. MRI is also used to monitor disease progression and to plan surgeries or radiation therapy.

Cathode Ray Tubes and Magnetic Fields

Cathode ray tubes (CRTs) were the display technology behind older TVs, computer monitors, and oscilloscopes. They demonstrate magnetic deflection of charged particles in a very direct way.

A CRT works like this:

1. An electron gun at the back of a vacuum tube emits a beam of electrons.
2. Electric fields accelerate and focus the beam.
3. Magnetic fields produced by deflection coils steer the beam horizontally and vertically, scanning it across a phosphorescent screen.
4. Where the beam strikes the screen, phosphor compounds emit visible light, building up an image point by point.

CRTs have been largely replaced by flat-panel displays, but the same principle of using magnetic fields to control electron beams appears in other technologies.

Traveling wave tubes (TWTs) and klystrons use magnetic fields for a different purpose: amplifying high-frequency signals. In a TWT, an electron beam travels through a helical structure alongside a radio-frequency (RF) signal. The beam transfers energy to the signal, amplifying it. A solenoid-style magnetic field keeps the electron beam focused and on track through the helix.

Electromagnetic Induction and Related Phenomena

Electromagnetic induction is the process of generating an electric current by changing the magnetic field through a circuit. It's the principle behind electric generators, transformers, and many sensors.

Two laws govern induction:

• Faraday's law says that a changing magnetic flux through a loop induces an electromotive force (EMF) in that loop. Magnetic flux ($\Phi_B$) measures the total magnetic field passing through a given area.
• Lenz's law says the induced current flows in whichever direction opposes the change in flux that created it. This is nature's way of resisting changes in magnetic flux and is consistent with conservation of energy.

A few related concepts often grouped with magnetism applications:

• The electromagnetic spectrum is the full range of electromagnetic radiation, from radio waves to visible light to X-rays. All of these are produced by accelerating charges or changing electromagnetic fields.
• Ferromagnetism is the strong form of magnetism found in materials like iron, cobalt, and nickel. In these materials, groups of atoms (called magnetic domains) align their magnetic moments in the same direction, producing a permanent magnetic field.