Magnetism
44 More Applications of Magnetism
Learning Objectives
- Explain how magnetic fields are used to separate charged particles according to their mass-to-charge ratio.
- Describe several biomedical and chemical applications of mass spectrometry.
- Describe how magnetic fields are used to steer and focus electron beams in medical and industrial devices.
- Explain the physical principles underlying Magnetic Resonance Imaging (MRI).
- Describe other medical applications of magnetic fields, including magnetocardiography (MCG), magnetoencephalography (MEG), and transcranial magnetic stimulation (TMS).
Mass Spectrometry
One of the most useful applications of magnetic fields is the ability to separate charged particles according to their mass. When a charged particle enters a magnetic field perpendicular to its velocity, the magnetic force causes it to follow a circular path. The radius of that path is
This equation shows that heavier particles travel in larger circles than lighter particles if they have the same speed, charge, and experience the same magnetic field. This principle forms the basis of a mass spectrometer, an instrument capable of identifying atoms, ions, and molecules by measuring their mass-to-charge ratio.
A typical mass spectrometer first converts the sample into charged particles (ions). These ions are accelerated and then pass through a velocity selector, which contains perpendicular electric and magnetic fields. Only ions moving at the correct speed experience equal and opposite electric and magnetic forces and continue into the analyzer. Since the electric force is [latex]F=qE[/latex] and the magnetic force is [latex]F=qvB[/latex], particles move straight through the selector only when
After canceling the charge, the selected velocity is
Once the ions enter a region containing only a magnetic field, they travel along circular paths whose radii depend on their mass-to-charge ratios. Measuring these radii allows the instrument to determine the identities of the particles in the sample. Mass spectrometry has become an indispensable tool in medicine, biology, chemistry, and forensic science. In clinical laboratories, it is used to identify drugs, hormones, vitamins, and disease biomarkers in blood and urine. It also plays an essential role in detecting metabolic disorders in newborns, monitoring therapeutic drug levels, identifying infectious microorganisms, and analyzing proteins involved in diseases such as cancer. Because it can distinguish molecules that differ by only a tiny amount in mass, mass spectrometry is one of the most sensitive analytical techniques available.
Electron Beams and Magnetic Steering
One important application of magnetic fields is controlling the motion of electron beams. Because electrons are charged particles, magnetic fields can bend and steer their paths without any physical contact. This principle is used in many scientific instruments and medical technologies.
Historically, magnetic steering was used in cathode-ray tubes (CRTs), the technology found in older televisions and computer monitors. In these devices, magnetic coils directed a beam of electrons across a fluorescent screen to create an image. Although CRT displays have largely been replaced by flat-panel technologies, the same physical principles remain important in many modern instruments. Today, magnetic steering is essential in electron microscopes, where magnetic lenses focus electron beams to produce images with much higher resolution than conventional light microscopes. Electron microscopy allows researchers to study viruses, bacteria, cells, and biological structures that are far too small to be seen with visible light. Magnetic fields are also used in particle accelerators, where they guide charged particles along carefully controlled paths. Many hospitals rely on accelerators called cyclotrons to produce short-lived radioactive isotopes used in positron emission tomography (PET) scans. Larger accelerators are also used in cancer treatment to generate high-energy radiation or proton beams for radiotherapy. Whether in a microscope, a medical imaging facility, or a research laboratory, magnetic fields provide a precise way to control the motion of charged particles. This ability to steer electrons and ions is one of the most important practical applications of magnetic forces.
Magnetic Resonance Imaging (MRI)
One of the most important medical applications of magnetism is magnetic resonance imaging (MRI). MRI is a noninvasive imaging technique that produces detailed two- and three-dimensional images of soft tissues without exposing patients to ionizing radiation such as X-rays or CT scans. It is widely used to diagnose injuries and diseases affecting the brain, spinal cord, joints, muscles, heart, and many internal organs. MRI is based on a phenomenon called nuclear magnetic resonance (NMR). Many atomic nuclei behave like tiny magnets because of a quantum property called spin. The hydrogen nucleus, which consists of a single proton, is especially useful because hydrogen is abundant in water and fat, making it one of the most common atoms in the human body. When a patient is placed inside the strong magnetic field of an MRI scanner, many of these tiny nuclear magnets become partially aligned with the field. A short pulse of radio-frequency (RF) energy is then applied at a specific resonance frequency, causing the protons to absorb energy and temporarily change their orientation. After the RF pulse is switched off, the protons gradually return to their original alignment. During this process they emit weak radio signals that are detected by receiver coils surrounding the patient. A computer analyzes these signals to reconstruct detailed cross-sectional images of the body. Modern MRI systems use powerful superconducting magnets that typically generate magnetic fields between 1.5 T and 3.0 T, although research systems may operate at even higher field strengths. Small magnetic field gradients are added to encode the position of the signals, allowing the scanner to determine where each signal originated inside the body and build highly detailed images. Different tissues return to equilibrium at different rates after the RF pulse. These differences produce image contrast and allow radiologists to distinguish between healthy and diseased tissue. Common MRI sequences include T1-weighted, T2-weighted, and proton-density imaging, each emphasizing different tissue characteristics. MRI is particularly valuable for imaging soft tissues, including the brain, spinal cord, ligaments, cartilage, muscles, and internal organs. It plays an essential role in diagnosing strokes, tumors, multiple sclerosis, sports injuries, spinal disorders, and many cardiovascular diseases. Because MRI uses radio waves rather than ionizing radiation, it can often be repeated safely when follow-up imaging is needed. A specialized technique called functional magnetic resonance imaging (fMRI) measures changes in blood oxygenation associated with neural activity. Active regions of the brain consume more oxygen, producing subtle changes in the magnetic properties of blood that MRI can detect. Researchers and clinicians use fMRI to study brain function, language, memory, movement, and decision making, as well as to plan certain neurosurgical procedures. Although MRI provides excellent images of soft tissues, it is not the best imaging technique for every situation. Conventional X-rays and CT scans remain superior for visualizing bone fractures and some lung conditions. For this reason, MRI complements rather than replaces other medical imaging technologies.
Other Medical Uses of Magnetic Fields
Magnetic fields generated by the human body provide valuable information about the activity of organs such as the heart and brain. Every time electrical currents flow through nerve cells or cardiac muscle, they also produce tiny magnetic fields. Although these fields are extremely weak—typically millions to hundreds of millions of times weaker than the Earth's magnetic field—they can be measured using highly sensitive detectors. Recording the magnetic field produced by the beating heart is called a magnetocardiogram (MCG), while measuring the magnetic fields generated by brain activity is known as a magnetoencephalogram (MEG). Unlike electrocardiograms (ECGs) and electroencephalograms (EEGs), which measure electrical voltages on the skin, MCG and MEG detect the magnetic fields produced by the same underlying electrical activity. Because magnetic fields are less distorted by surrounding tissues than electrical signals, these techniques can sometimes provide complementary diagnostic information. One important advantage of MCG and MEG is that the sensors do not need to make direct contact with the patient's body. MCG has been investigated for detecting abnormal heart rhythms, evaluating reduced blood flow to the heart, and monitoring fetal heart activity during pregnancy. Similarly, MEG allows physicians and researchers to study brain function in real time and has become an important tool for locating regions responsible for epilepsy before surgery, investigating Alzheimer's disease, and studying how different parts of the brain process language, memory, and movement. These measurements are possible because of extremely sensitive instruments called superconducting quantum interference devices (SQUIDs). SQUID sensors operate at cryogenic temperatures and are capable of detecting magnetic fields thousands of times weaker than the Earth's magnetic field. Newer technologies based on optically pumped magnetometers are also being developed, allowing some modern MEG systems to operate without the need for liquid helium cooling. Magnetic fields are also used therapeutically. For example, transcranial magnetic stimulation (TMS) uses rapidly changing magnetic fields to induce small electric currents in specific regions of the brain. TMS is now an established treatment for some patients with major depressive disorder and is also being investigated for conditions such as obsessive-compulsive disorder, chronic pain, stroke rehabilitation, and certain neurological disorders.
Evidence-Based Medicine
Commercial products such as magnetic bracelets, necklaces, mattress pads, and shoe inserts are often marketed with claims that they improve circulation, reduce pain, increase energy, or treat a variety of medical conditions. Although these products are generally harmless for most people, high-quality clinical studies have not demonstrated consistent health benefits beyond placebo effects. At present, there is no well-established biological mechanism that explains the broad therapeutic claims made for these products. People with implanted medical devices such as pacemakers, implantable cardioverter-defibrillators (ICDs), cochlear implants, or certain insulin pumps should consult their healthcare provider before using strong permanent magnets, since sufficiently strong magnetic fields may interfere with the normal operation of these devices.
Interactive Exploration: Magnet and Compass
A compass works because its needle is a small permanent magnet that aligns with the magnetic field at its location. In this simulation, you will explore how a compass responds to the magnetic field produced by a bar magnet and compare it with Earth's magnetic field. You will also investigate how magnetic field strength changes with distance and with the strength of the magnet. Move the compass to different locations around the magnet and observe how the needle always aligns with the local magnetic field. Use the magnetic field meter to measure the field strength, change the strength of the magnet, and turn Earth's magnetic field on and off to see how multiple magnetic fields combine. As you work through the simulation, relate your observations to the magnetic field lines and to Right-Hand Rule 2 introduced earlier in this chapter.
Guided Exploration
As you interact with the simulation, try to answer the following questions:
- Move the compass around the bar magnet. How does the compass needle change direction at different locations?
- Where is the magnetic field strongest? What observations from the field meter or field lines support your answer?
- Move the compass farther away from the magnet. How do the strength and direction of the magnetic field change with distance?
- Increase and decrease the strength of the magnet. How does this affect both the compass needle and the measured magnetic field?
- Turn on Earth's magnetic field. How does the compass behave when both the bar magnet and Earth's field are present?
- Place the compass far away from the bar magnet. Why does it point approximately north?
- Explain why placing a magnet close to a compass can cause navigation errors.
After completing the exploration, compare your observations with the concepts presented in this chapter. A compass always aligns with the net magnetic field acting on it. Close to a strong magnet, the magnet's field dominates the direction of the compass needle. Far from nearby magnets, Earth's magnetic field is the strongest field present, causing the compass to point approximately toward magnetic north.
Life Sciences Connection: Magnetoreception in Migratory Animals
Many animals sense the Earth's weak magnetic field (about 25 to 65 microtesla at the surface) and use it to navigate during long-distance migration. Migratory songbirds are thought to sense the field's inclination angle—the angle between the field lines and the ground—using light-sensitive proteins called cryptochromes in their eyes, in a chemical process that may be affected by quantum spin states of electron pairs. Sea turtles use a different strategy, sensing both the field's intensity and inclination angle to build an internal "magnetic map" of the coastline, allowing a hatchling to swim thousands of kilometers across open ocean and, years later, return to nest on the same beach where it hatched. Some migratory fish and mole rats, meanwhile, appear to rely on tiny magnetite crystals embedded in specialized cells, which physically twist in response to an external field much like a compass needle. Because these magnetic senses are so subtle, biologists studying them often use the same physics that describes MRI and magnetic steering in this chapter—field strength, field gradients, and magnetic torque on a dipole—to design experiments that isolate how animals detect and respond to magnetic fields.
Section Summary
- Crossed (perpendicular) electric and magnetic fields can act as a velocity selector. A charged particle moving perpendicular to both fields will travel in a straight line only if the electric and magnetic forces are equal in magnitude and opposite in direction.
- The speed of particles that pass through a velocity selector is
[latex]v=\frac{E}{B},[/latex]
where [latex]E[/latex] is the electric field strength and [latex]B[/latex] is the magnetic field strength.
- Velocity selectors are important components of many scientific instruments, including mass spectrometers, where they ensure that only particles with a specific speed enter the analyzing region.
- Magnetic fields are widely used in medicine and technology, including magnetic resonance imaging (MRI), magnetoencephalography (MEG), magnetocardiography (MCG), and the steering of charged particles in devices such as electron microscopes and particle accelerators.
Conceptual Questions
- Measurements of the weak and fluctuating magnetic fields associated with brain activity are called magnetoencephalograms (MEGs). Do the brain's magnetic fields imply coordinated or uncoordinated nerve impulses? Explain.
- Discuss the possibility that a Hall voltage would be generated in the moving heart of a patient during an MRI examination. Also discuss the same effect on the wires of a pacemaker. (The fact that patients with pacemakers are generally not given MRI scans is significant.)
- A patient inside an MRI scanner quickly turns their head and experiences temporary dizziness and a strange metallic taste. Discuss possible physical explanations for these sensations.
- You are told that a certain region contains either a uniform electric field or a uniform magnetic field. What observation or measurement could you make to determine which type of field is present? (Ignore Earth's magnetic field.)
- An example of magnetohydrodynamics (MHD) occurs when salty river water flows through Earth's magnetic field, producing a potential difference between the river banks. Describe how you would calculate this potential difference.
- Draw gravitational field lines between two masses, electric field lines between a positive and a negative charge, electric field lines between two positive charges, and magnetic field lines around a bar magnet. Describe the major differences between these field patterns and explain what physical objects produce each type of field.
Problems & Exercises
- Indicate whether the magnetic field created in each of the three situations shown in Figure 44.4 is into or out of the page on the left and right of the current.
Figure 44.4. - What are the directions of the fields in the center of the loop and coils shown in Figure 44.5?
Figure 44.5. - What are the directions of the currents in the loop and coils shown in Figure 44.6?
Figure 44.6. - To see why an MRI utilizes iron to increase the magnetic field created by a coil, calculate the current needed in a 400-loop-per-meter circular coil 0.660 m in radius to create a 1.20-T field (typical of an MRI instrument) at its center with no iron present. The magnetic field of a proton is approximately like that of a circular current loop [latex]0.650\times10^{-15}\ \text{m}[/latex] in radius carrying [latex]1.05\times10^{4}\ \text{A}[/latex]. What is the field at the center of such a loop?
- Inside a motor, 30.0 A passes through a 250-turn circular loop that is 10.0 cm in radius. What is the magnetic field strength created at its center?
- Nonnuclear submarines use batteries for power when submerged.
- Find the magnetic field 50.0 cm from a straight wire carrying 1200 A from the batteries to the drive mechanism of a submarine.
- What is the field if the wires to and from the drive mechanism are side by side?
- Discuss the effects this could have for a compass on the submarine that is not shielded.
- How strong is the magnetic field inside a solenoid with 10,000 turns per meter that carries 20.0 A?
- What current is needed in the solenoid described in Problem 64 to produce a magnetic field [latex]10^{4}[/latex] times the Earth’s magnetic field of [latex]5.00\times10^{-5}\ \text{T}[/latex]?
- How far from the starter cable of a car, carrying 150 A, must you be to experience a field less than the Earth’s [latex]\left(5.00\times10^{-5}\ \text{T}\right)[/latex]? Assume a long straight wire carries the current. (In practice, the body of your car shields the dashboard compass.)
- Measurements affect the system being measured, such as the current loop discussed previously.
- Estimate the field the loop creates by calculating the field at the center of a circular loop 20.0 cm in diameter carrying 5.00 A.
- What is the smallest field strength this loop can be used to measure, if its field must alter the measured field by less than 0.0100%?
- Figure 44.7 shows a long straight wire just touching a loop carrying a current [latex]I_1[/latex]. Both lie in the same plane.
- What direction must the current [latex]I_2[/latex] in the straight wire have to create a field at the center of the loop in the direction opposite to that created by the loop?
- What is the ratio of [latex]I_1/I_2[/latex] that gives zero field strength at the center of the loop?
- What is the direction of the field directly above the loop under this circumstance?
Figure 44.7. - Find the magnitude and direction of the magnetic field at the point equidistant from the wires in Figure 43.5(a), using the rules of vector addition to sum the contributions from each wire.
- Find the magnitude and direction of the magnetic field at the point equidistant from the wires in Figure 43.5(b), using the rules of vector addition to sum the contributions from each wire.
- What current is needed in the top wire in Figure 43.5(a) to produce a field of zero at the point equidistant from the wires, if the currents in the bottom two wires are both 10.0 A into the page?
- Calculate the size of the magnetic field 20 m below a high-voltage power line. The line carries 450 MW at a voltage of 300,000 V.
- Integrated Concepts
- A pendulum is set up so that its bob (a thin copper disk) swings between the poles of a permanent magnet as shown in Figure 44.8. What is the magnitude and direction of the magnetic force on the bob at the lowest point in its path, if it has a positive [latex]0.250\ \mu\text{C}[/latex] charge and is released from a height of 30.0 cm above its lowest point? The magnetic field strength is 1.50 T.
- What is the acceleration of the bob at the bottom of its swing if its mass is 30.0 grams and it is hung from a flexible string? Be certain to include a free-body diagram as part of your analysis.
Figure 44.8. - Integrated Concepts
- What voltage will accelerate electrons to a speed of [latex]6.00\times10^{-7}\ \text{m/s}[/latex]?
- Find the radius of curvature of the path of a proton accelerated through this potential in a 0.500-T field and compare this with the radius of curvature of an electron accelerated through the same potential.
- Integrated ConceptsFind the radius of curvature of the path of a 25.0-MeV proton moving perpendicularly to the 1.20-T field of a cyclotron.
- Integrated ConceptsTo construct a nonmechanical water meter, a 0.500-T magnetic field is placed across the supply water pipe to a home and the Hall voltage is recorded.
- Find the flow rate in liters per second through a 3.00-cm-diameter pipe if the Hall voltage is 60.0 mV.
- What would the Hall voltage be for the same flow rate through a 10.0-cm-diameter pipe with the same field applied?
- Integrated Concepts
- Using the values given for the MHD drive discussed previously, and assuming the force is uniformly applied to the fluid, calculate the pressure created in [latex]\text{N/m}^{2}[/latex].
- Is this a significant fraction of an atmosphere?
- Integrated Concepts
- Calculate the maximum torque on a 50-turn, 1.50 cm radius circular current loop carrying [latex]50\ \mu\text{A}[/latex] in a 0.500-T field.
- If this coil is to be used in a galvanometer that reads [latex]50\ \mu\text{A}[/latex] full scale, what force constant spring must be used, if it is attached 1.00 cm from the axis of rotation and is stretched by the [latex]60^\circ[/latex] arc moved?
- Integrated ConceptsA current balance used to define the ampere is designed so that the current through it is constant, as is the distance between wires. Even so, if the wires change length with temperature, the force between them will change. What percent change in force per degree will occur if the wires are copper?
- Integrated Concepts
- Show that the period of the circular orbit of a charged particle moving perpendicularly to a uniform magnetic field is [latex]T=2\pi m/(qB)[/latex].
- What is the frequency [latex]f[/latex]?
- What is the angular velocity [latex]\omega[/latex]?
Note that these results are independent of the velocity and radius of the orbit and, hence, of the energy of the particle. See Figure 44.9.
Figure 44.9: Cyclotrons accelerate charged particles orbiting in a magnetic field by placing an AC voltage on the metal dees, between which the particles move, so that energy is added twice each orbit. The frequency is constant, since it is independent of the particle energy—the radius of the orbit simply increases with energy until the particles approach the edge and are extracted for various experiments and applications. - Integrated ConceptsA cyclotron accelerates charged particles as shown in Figure 44.9. Using the results of the previous problem, calculate the frequency of the accelerating voltage needed for a proton in a 1.20-T field.
- Integrated Concepts
- A 0.140-kg baseball, pitched at 40.0 m/s horizontally and perpendicular to the Earth’s horizontal [latex]5.00\times10^{-5}\ \text{T}[/latex] field, has a 100-nC charge on it. What distance is it deflected from its path by the magnetic force, after traveling 30.0 m horizontally?
- Would you suggest this as a secret technique for a pitcher to throw curve balls?
- Integrated Concepts
- What is the direction of the force on a wire carrying a current due east in a location where the Earth’s field is due north? Both are parallel to the ground.
- Calculate the force per meter if the wire carries 20.0 A and the field strength is [latex]3.00\times10^{-5}\ \text{T}[/latex].
- What diameter copper wire would have its weight supported by this force?
- Calculate the resistance per meter and the voltage per meter needed.
- Integrated ConceptsOne long straight wire is to be held directly above another by repulsion between their currents. The lower wire carries 100 A and the wire 7.50 cm above it is 10-gauge (2.588 mm diameter) copper wire.
- What current must flow in the upper wire, neglecting the Earth’s field?
- What is the smallest current if the Earth’s [latex]3.00\times10^{-5}\ \text{T}[/latex] field is parallel to the ground and is not neglected?
- Is the supported wire in a stable or unstable equilibrium if displaced vertically? If displaced horizontally?
- Unreasonable Results
- Find the charge on a baseball, thrown at 35.0 m/s perpendicular to the Earth’s [latex]5.00\times10^{-5}\ \text{T}[/latex] field, that experiences a 1.00-N magnetic force.
- What is unreasonable about this result?
- Which assumption or premise is responsible?
- Unreasonable ResultsA charged particle having mass [latex]6.64\times10^{-27}\ \text{kg}[/latex] (that of a helium atom) moving at [latex]8.70\times10^{5}\ \text{m/s}[/latex] perpendicular to a 1.50-T magnetic field travels in a circular path of radius 16.0 mm.
- What is the charge of the particle?
- What is unreasonable about this result?
- Which assumptions are responsible?
- Unreasonable ResultsAn inventor wants to generate 120-V power by moving a 1.00-m-long wire perpendicular to the Earth’s [latex]5.00\times10^{-5}\ \text{T}[/latex] field.
- Find the speed with which the wire must move.
- What is unreasonable about this result?
- Which assumption is responsible?
- Unreasonable ResultsFrustrated by the small Hall voltage obtained in blood flow measurements, a medical physicist decides to increase the applied magnetic field strength to get a 0.500-V output for blood moving at 30.0 cm/s in a 1.50-cm-diameter vessel.
- What magnetic field strength is needed?
- What is unreasonable about this result?
- Which premise is responsible?
- Unreasonable ResultsA surveyor 100 m from a long straight 200-kV DC power line suspects that its magnetic field may equal that of the Earth and affect compass readings.
- Calculate the current in the wire needed to create a [latex]5.00\times10^{-5}\ \text{T}[/latex] field at this distance.
- What is unreasonable about this result?
- Which assumption or premise is responsible?
- Construct Your Own ProblemConsider a mass separator that applies a magnetic field perpendicular to the velocity of ions and separates the ions based on the radius of curvature of their paths in the field. Construct a problem in which you calculate the magnetic field strength needed to separate two ions that differ in mass, but not charge, and have the same initial velocity. Among the things to consider are the types of ions, the velocities they can be given before entering the magnetic field, and a reasonable value for the radius of curvature of the paths they follow. In addition, calculate the separation distance between the ions at the point where they are detected.
- Construct Your Own ProblemConsider using the torque on a current-carrying coil in a magnetic field to detect relatively small magnetic fields (less than the field of the Earth, for example). Construct a problem in which you calculate the maximum torque on a current-carrying loop in a magnetic field. Among the things to be considered are the size of the coil, the number of loops it has, the current you pass through the coil, and the size of the field you wish to detect. Discuss whether the torque produced is large enough to be effectively measured. Your instructor may also wish for you to consider the effects, if any, of the field produced by the coil on the surroundings that could affect detection of the small field.
Glossary
- magnetic resonance imaging (MRI)
- A noninvasive medical imaging technique that uses strong magnetic fields and radio waves to produce detailed images of internal organs and soft tissues without using ionizing radiation.
- nuclear magnetic resonance (NMR)
- A physical phenomenon in which atomic nuclei interact with an external magnetic field and absorb and reemit radio-frequency energy at specific resonant frequencies. MRI is based on this principle.
- magnetocardiogram (MCG)
- A recording of the extremely weak magnetic fields produced by the electrical activity of the heart during each heartbeat.
- magnetoencephalogram (MEG)
- A recording of the extremely weak magnetic fields generated by electrical activity in the brain, used to study brain function and diagnose certain neurological disorders.
A noninvasive medical imaging technique that uses strong magnetic fields and radio waves to produce detailed images of internal organs and soft tissues without using ionizing radiation.
A physical phenomenon in which atomic nuclei interact with an external magnetic field and absorb and reemit radio-frequency energy at specific resonant frequencies. MRI is based on this principle.
A recording of the extremely weak magnetic fields produced by the electrical activity of the heart during each heartbeat.
A recording of the extremely weak magnetic fields generated by electrical activity in the brain, used to study brain function and diagnose certain neurological disorders.
