It was noted that this relationship could be used to measure the mass of charged particles such as ions. The velocity selector has both an electric field and a magnetic field, perpendicular to one another, producing forces in opposite directions on the ions. Mass spectrometry today is used extensively in chemistry and biology laboratories to identify chemical and biological substances according to their mass-to-charge ratios. What do non-flat-screen TVs, old computer monitors, x-ray machines, and the 2-mile-long Stanford Linear Accelerator have in common?
Magnetic resonance imaging (MRI) is one of the most useful and rapidly growing medical imaging tools. When placed in an external magnetic field, such nuclei experience a torque that pushes or aligns the nuclei into one of two new energy states—depending on the orientation of its spin (analogous to the N pole and S pole in a bar magnet). The largest part of the MRI unit is a superconducting magnet that creates a magnetic field, typically between 1 and 2 T in strength, over a relatively large volume.
An image requires position information as well as the density of a nuclear type (usually protons).
While MRI images are superior to x rays for certain types of tissue and have none of the hazards of x rays, they do not completely supplant x-ray images. Over the last decade, the development of much faster scans, called “functional MRI” (fMRI), has allowed us to map the functioning of various regions in the brain responsible for thought and motor control. MEG can be used to identify abnormal electrical discharges in the brain that produce weak magnetic signals. Finally, there is a burgeoning market for magnetic cures in which magnets are applied in a variety of ways to the body, from magnetic bracelets to magnetic mattresses. Measurements of the weak and fluctuating magnetic fields associated with brain activity are called magnetoencephalograms (MEGs). Discuss the possibility that a Hall voltage would be generated on the moving heart of a patient during MRI imaging. A patient in an MRI unit turns his head quickly to one side and experiences momentary dizziness and a strange taste in his mouth.
You are told that in a certain region there is either a uniform electric or magnetic field. Draw gravitational field lines between 2 masses, electric field lines between a positive and a negative charge, electric field lines between 2 positive charges and magnetic field lines around a magnet. Indicate whether the magnetic field created in each of the three situations shown in [link] is into or out of the page on the left and right of the current. How strong is the magnetic field inside a solenoid with 10,000 turns per meter that carries 20.0 A?
How far from the starter cable of a car, carrying 150 A, must you be to experience a field less than the Earth’s (5.00?10?5T)? Find the magnitude and direction of the magnetic field at the point equidistant from the wires in [link](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 [link](b), using the rules of vector addition to sum the contributions from each wire. What current is needed in the top wire in [link](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? To 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.
A current balance used to define the ampere is designed so that the current through it is constant, as is the distance between wires. One long straight wire is to be held directly above another by repulsion between their currents.
A 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.
Consider 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.


Consider 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).
Only those ions for which the forces balance travel in a straight line into the next region. In medicine, mass spectrometers are used to measure the concentration of isotopes used as tracers. It non-invasively produces two-dimensional and three-dimensional images of the body that provide important medical information with none of the hazards of x-rays.
Transitions from the lower to higher energy state can be achieved by using an external radio frequency signal to “flip” the orientation of the small magnets.
MRI images can be both highly detailed and informative about structures and organ functions. By varying the magnetic field slightly over the volume to be imaged, the resonant frequency of the protons is made to vary with position. MRI is less effective than x rays for detecting breaks in bone, for example, and in imaging breast tissue, so the two diagnostic tools complement each other. This technique measures the change in blood flow for activities (thought, experiences, action) in the brain. Recording of the heart’s magnetic field as it beats is called a magnetocardiogram (MCG), while measurements of the brain’s magnetic field is called a magnetoencephalogram (MEG). The best that can be said for such practices is that they are apparently harmless, unless the magnets get close to the patient’s computer or magnetic storage disks. Explore the interactions between a compass and bar magnet, and then add the Earth and find the surprising answer! This fluid interacts with the Earth’s magnetic field to produce a potential difference between the two river banks.
Qualitatively describe the differences between the fields and the entities responsible for the field lines. Using the results of the previous problem, calculate the frequency of the accelerating voltage needed for a proton in a 1.20-T field. What distance is it deflected from its path by the magnetic force, after traveling 30.0 m horizontally?
It implies a total power delivery in the line of 50.0x10^9 W, which is much too high for standard transmission lines. Also coaxial cables are used for transmission lines so that there is virtually no field for DC power lines, because of cancellation from opposing currents. 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.
Construct a problem in which you calculate the maximum torque on a current-carrying loop in a magnetic field. Most mass spectrometers use magnetic fields for this purpose, although some of them have extremely sophisticated designs. Usually, biological molecules such as proteins are very large, so they are broken down into smaller fragments before analyzing. MRI is based on an effect called nuclear magnetic resonance (NMR) in which an externally applied magnetic field interacts with the nuclei of certain atoms, particularly those of hydrogen (protons).
It is helpful that normal and non-normal tissues respond differently for slight changes in the magnetic field.
Broadcast radio frequencies are swept over an appropriate range and nuclei absorb and reemit them only if the nuclei are in a magnetic field with the correct strength. MRI images are also expensive compared to simple x-ray images and tend to be used most often where they supply information not readily obtained from x rays.
Both give information that differs from that obtained by measuring the electric fields of these organs (ECGs and EEGs), but they are not yet of sufficient importance to make these difficult measurements common. MCG also looks at the heart’s electrical activity whose voltage output is too small to be recorded by surface electrodes as in EKG.


Claims are made for a broad spectrum of benefits from cleansing the blood to giving the patient more energy, but clinical studies have not verified these claims, nor is there an identifiable mechanism by which such benefits might occur. 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. 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. These nuclei possess their own small magnetic fields, similar to those of electrons and the current loops discussed earlier in this chapter. The imaging receiver gathers information through the body almost point by point, building up a tissue map. Another disadvantage of MRI is that the patient is totally enclosed with detectors close to the body for about 30 minutes or more, leading to claustrophobia. Blood hemoglobin releases oxygen to active nerve cells and has somewhat different magnetic properties when oxygenated than when deoxygenated. It has the potential of being a rapid scan for early diagnosis of cardiac ischemia (obstruction of blood flow to the heart) or problems with the fetus.
Advances in instrumentation to measure very small magnetic fields have allowed these two techniques to be used more in recent years. In addition, calculate the separation distance between the ions at the point where they are detected. Sometimes a gas chromatograph or high-performance liquid chromatograph provides an initial separation of the large molecules, which are then input into the mass spectrometer.
Two pairs of coils are used to steer the electrons, one vertically and the other horizontally, to their desired destination.
We will return to these topics in later chapters.) The specific frequency of the radio waves that are absorbed and reemitted depends sensitively on the type of nucleus, the chemical environment, and the external magnetic field strength.
Over the past two decades, NMR has been developed to produce detailed images in a process now called magnetic resonance imaging (MRI), a name coined to avoid the use of the word “nuclear” and the concomitant implication that nuclear radiation is involved. The reception of reemitted radio waves as a function of frequency thus gives position information. 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.
Therefore, this is a resonance phenomenon in which nuclei in a magnetic field act like resonators (analogous to those discussed in the treatment of sound in Oscillatory Motion and Waves) that absorb and reemit only certain frequencies. MRI can also be used to follow the movement of certain ions across membranes, yielding information on active transport, osmosis, dialysis, and other phenomena. New “open-MRI” machines are now available in which the magnet does not completely surround the patient.
This operates at liquid helium temperatures and can measure magnetic fields thousands of times smaller than the Earth’s. With excellent spatial resolution, MRI can provide information about tumors, strokes, shoulder injuries, infections, etc. The intensity of the reemitted radio waves is proportional to the concentration of the nuclear type being flipped, as well as information on the chemical environment in that area of the body. Various techniques are available for enhancing contrast in images and for obtaining more information.
Scans called T1, T2, or proton density scans rely on different relaxation mechanisms of nuclei. Relaxation refers to the time it takes for the protons to return to equilibrium after the external field is turned off.



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