#set document(title: "22.2 Ferromagnets and Electromagnets", author: "OpenStax / XYZ Homework") #set page(width: 8.5in, height: auto, margin: 1in) #import "@preview/cetz:0.5.2" #set text(font: ("STIX Two Text", "Libertinus Serif", "New Computer Modern"), size: 10.5pt, lang: "en") #show math.equation: set text(font: ("STIX Two Math", "New Computer Modern Math")) #set par(justify: true, leading: 0.62em, spacing: 0.9em) #set enum(spacing: 1.1em) // room between list items so tall inline fractions don't collide #set list(spacing: 1.1em) #set table(stroke: 0.5pt + rgb("#c7ccd3")) #let BLUE = rgb("#183B6F") // brand navy — section bars + example/solution labels (white on navy 11.09:1) #let ORANGE = rgb("#A94509") // brand primary-700 — AA-safe deep orange for TEXT (5.93:1 on white; raw brand #F37021 is 2.94:1 and must never carry text) #let RED = rgb("#DC2626") // brand error-600 #let GREEN = rgb("#059669") // brand success-600 (decoration only; small green text uses green-text #007942) #show heading.where(level: 1): it => block(width: 100%, above: 0pt, below: 16pt, fill: gradient.linear(BLUE, rgb("#2C5AA0")), inset: (x: 14pt, y: 12pt), radius: 3pt, text(fill: white, weight: "bold", size: 19pt, it.body)) #show heading.where(level: 2): it => block(width: 100%, above: 18pt, below: 10pt, fill: BLUE, inset: (x: 10pt, y: 6pt), radius: 2pt, text(fill: white, weight: "bold", size: 12pt, it.body)) #show heading.where(level: 3): it => text(fill: ORANGE, weight: "bold", size: 12.5pt, it.body) #show heading.where(level: 4): it => text(fill: BLUE, weight: "bold", size: 10.5pt, it.body) #let examplebox(label, title, body) = block(width: 100%, breakable: true, fill: rgb("#EFF1F5"), stroke: 0.5pt + rgb("#CFDDF0"), radius: 4pt, inset: 10pt, above: 12pt, below: 12pt)[ #block(below: 6pt)[#box(fill: BLUE, inset: (x: 6pt, y: 2pt), radius: 2pt, text(fill: white, weight: "bold", size: 8.5pt, label)) #h(0.4em) #strong[#title]] #body] // rail = decorative left rule (raw brand token); labelcolor = AA-safe label text shade #let notebox(label, rail, labelcolor, tint, body) = block(width: 100%, breakable: true, fill: tint, stroke: (left: 3pt + rail), inset: (left: 10pt, rest: 8pt), radius: (right: 4pt), above: 11pt, below: 11pt)[ #text(fill: labelcolor, weight: "bold", size: 7.5pt, tracking: 0.5pt)[#upper(label)] #linebreak() #body] #let solutionbox(body) = block(above: 4pt, below: 8pt)[ #text(fill: BLUE, weight: "bold", size: 8.5pt)[Solution] #linebreak() #body] #let figph(msg) = block(width: 100%, height: 60pt, fill: rgb("#f6f7f9"), stroke: (paint: rgb("#c7ccd3"), dash: "dashed"), radius: 4pt, inset: 10pt)[ #align(center + horizon, text(fill: rgb("#889"), style: "italic", size: 9pt, msg))] // Standardize inlined figure sizes: measure the natural CeTZ canvas, then scale to a // consistent envelope (aspect-aware; see build_typst.py FIG_* constants). Unlike the // print preamble, dimensions are FLOORED: in an editor a user can trim a figure to a // degenerate 1-D shape (a bare line), and w/h or tw/w would then divide by zero. #let _STD_W = 3.5 #let _WIDE_W = 5.6 #let _MAX_H = 3.4 #let _ASPECT_WIDE = 2.2 #let _UPSCALE_MAX = 1.15 #let stdfig(body) = context { let m = measure(body) let w = calc.max(m.width / 1in, 0.01) let h = calc.max(m.height / 1in, 0.01) let tw = if w / h > _ASPECT_WIDE { _WIDE_W } else { _STD_W } let s = calc.min(tw / w, _MAX_H / h, _UPSCALE_MAX) align(center, box(scale(x: s * 100%, y: s * 100%, reflow: true, body))) } #show figure: set block(breakable: false) #set figure(gap: 8pt) #show figure.caption: set text(size: 8.5pt, fill: rgb("#555")) == 22.2#h(0.6em)Ferromagnets and Electromagnets === Learning Objectives By the end of this section, you will be able to: - Define ferromagnet. - Describe the role of magnetic domains in magnetization. - Explain the significance of the Curie temperature. - Describe the relationship between electricity and magnetism. === Ferromagnets Only certain materials, such as iron, cobalt, nickel, and gadolinium, exhibit strong magnetic effects. Such materials are called #strong[ferromagnetic], after the Latin word for iron, #emph[ferrum]. A group of materials made from the alloys of the rare earth elements are also used as strong and permanent magnets; a popular one is neodymium. Other materials exhibit weak magnetic effects, which are detectable only with sensitive instruments. Not only do ferromagnetic materials respond strongly to magnets (the way iron is attracted to magnets), they can also be #strong[magnetized] themselves—that is, they can be induced to be magnetic or made into permanent magnets. #figure(figph[An unmagnetized piece of iron is turned into a permanent magnet using heat and another magnet.], alt: "An unmagnetized piece of iron is turned into a permanent magnet using heat and another magnet.", caption: [An unmagnetized piece of iron is placed between two magnets, heated, and then cooled, or simply tapped when cold. The iron becomes a permanent magnet with the poles aligned as shown: its south pole is adjacent to the north pole of the original magnet, and its north pole is adjacent to the south pole of the original magnet. Note that there are attractive forces between the magnets.]) When a magnet is brought near a previously unmagnetized ferromagnetic material, it causes local magnetization of the material with unlike poles closest, as in . (This results in the attraction of the previously unmagnetized material to the magnet.) What happens on a microscopic scale is illustrated in . The regions within the material called #strong[domains] act like small bar magnets. Within domains, the poles of individual atoms are aligned. Each atom acts like a tiny bar magnet. Domains are small and randomly oriented in an unmagnetized ferromagnetic object. In response to an external magnetic field, the domains may grow to millimeter size, aligning themselves as shown in (b). This induced magnetization can be made permanent if the material is heated and then cooled, or simply tapped in the presence of other magnets. #figure(figph[Three schematic diagrams of a piece of iron showing magnetic domains. In Figure a, there are many domains (tiny magnetic regions, each with a north pole and a south pole). Each domain has a slightly different orientation. In Figure b, the domains are larger. Most of the domains are oriented in roughly the same direction. In Figure c, there is a single domain for the entire piece of iron. There is a north pole and a south pole.], alt: "Three schematic diagrams of a piece of iron showing magnetic domains. In Figure a, there are many domains (tiny magnetic regions, each with a north pole and a south pole). Each domain has a slightly different orientation. In Figure b, the domains are larger. Most of the domains are oriented in roughly the same direction. In Figure c, there is a single domain for the entire piece of iron. There is a north pole and a south pole.", caption: [(a) An unmagnetized piece of iron (or other ferromagnetic material) has randomly oriented domains. (b) When magnetized by an external field, the domains show greater alignment, and some grow at the expense of others. Individual atoms are aligned within domains; each atom acts like a tiny bar magnet.]) Conversely, a permanent magnet can be demagnetized by hard blows or by heating it in the absence of another magnet. Increased thermal motion at higher temperature can disrupt and randomize the orientation and the size of the domains. There is a well-defined temperature for ferromagnetic materials, which is called the #strong[Curie temperature], above which they cannot be magnetized. The Curie temperature for iron is 1043 K #math.equation(block: false, alt: "open parenthesis 770ºC close parenthesis")[$( "770ºC" )$], which is well above room temperature. There are several elements and alloys that have Curie temperatures much lower than room temperature and are ferromagnetic only below those temperatures. === Electromagnets Early in the 19th century, it was discovered that electrical currents cause magnetic effects. The first significant observation was by the Danish scientist Hans Christian Oersted (1777–1851), who found that a compass needle was deflected by a current-carrying wire. This was the first significant evidence that the movement of charges had any connection with magnets. #strong[Electromagnetism] is the use of electric current to make magnets. These temporarily induced magnets are called #strong[electromagnets]. Electromagnets are employed for everything from a wrecking yard crane that lifts scrapped cars to controlling the beam of a 90-km-circumference particle accelerator to the magnets in medical imaging machines. #figure(figph[M R I machine at a hospital.], alt: "M R I machine at a hospital.", caption: [Instrument for magnetic resonance imaging (MRI). The device uses a superconducting cylindrical coil for the main magnetic field. The patient goes into this “tunnel” on the gurney.]) shows that the response of iron filings to a current-carrying coil and to a permanent bar magnet. The patterns are similar. In fact, electromagnets and ferromagnets have the same basic characteristics—for example, they have north and south poles that cannot be separated and for which like poles repel and unlike poles attract. #figure(figph[The arrangement of iron filings as they are affected by a metal coil that is carrying an electric current and a bar magnet. At the poles of the magnet, the filings are aligned radially to the poles. Between the poles, the filings are roughly parallel to the magnet. Thus, from one pole to the other, the filings have an arcuate arrangement. The density of filings is very high at the poles and relatively low on either side of the center of the magnet. The arrangement is similar around the current-carrying coil.], alt: "The arrangement of iron filings as they are affected by a metal coil that is carrying an electric current and a bar magnet. At the poles of the magnet, the filings are aligned radially to the poles. Between the poles, the filings are roughly parallel to the magnet. Thus, from one pole to the other, the filings have an arcuate arrangement. The density of filings is very high at the poles and relatively low on either side of the center of the magnet. The arrangement is similar around the current-carrying coil.", caption: [Iron filings near (a) a current-carrying coil and (b) a magnet act like tiny compass needles, showing the shape of their fields. Their response to a current-carrying coil and a permanent magnet is seen to be very similar, especially near the ends of the coil and the magnet.]) Combining a ferromagnet with an electromagnet can produce particularly strong magnetic effects. () Whenever strong magnetic effects are needed, such as lifting scrap metal, or in particle accelerators, electromagnets are enhanced by ferromagnetic materials. Limits to how strong the magnets can be made are imposed by coil resistance (it will overheat and melt at sufficiently high current), and so superconducting magnets may be employed. These are still limited, because superconducting properties are destroyed by too great a magnetic field. #figure(figph[An electrical current runs through a metal wire that is coiled around a ferromagnet.], alt: "An electrical current runs through a metal wire that is coiled around a ferromagnet.", caption: [An electromagnet with a ferromagnetic core can produce very strong magnetic effects. Alignment of domains in the core produces a magnet, the poles of which are aligned with the electromagnet.]) shows a few uses of combinations of electromagnets and ferromagnets. Ferromagnetic materials can act as memory devices, because the orientation of the magnetic fields of small domains can be reversed or erased. Magnetic information storage on videotapes and computer hard drives are among the most common applications. This property is vital in our digital world. #figure(figph[Three views into a computer disk showing the magnetic portions of the recording head and the tape.], alt: "Three views into a computer disk showing the magnetic portions of the recording head and the tape.", caption: [An electromagnet induces regions of permanent magnetism on a floppy disk coated with a ferromagnetic material. The information stored here is digital (a region is either magnetic or not); in other applications, it can be analog (with a varying strength), such as on audiotapes.]) === Current: The Source of All Magnetism An electromagnet creates magnetism with an electric current. In later sections we explore this more quantitatively, finding the strength and direction of magnetic fields created by various currents. But what about ferromagnets? shows models of how electric currents create magnetism at the submicroscopic level. (Note that we cannot directly observe the paths of individual electrons about atoms, and so a model or visual image, consistent with all direct observations, is made. We can directly observe the electron’s orbital angular momentum, its spin momentum, and subsequent magnetic moments, all of which are explained with electric-current-creating subatomic magnetism.) Currents, including those associated with other submicroscopic particles like protons, allow us to explain ferromagnetism and all other magnetic effects. Ferromagnetism, for example, results from an internal cooperative alignment of electron spins, possible in some materials but not in others. Crucial to the statement that electric current is the source of all magnetism is the fact that it is impossible to separate north and south magnetic poles. (This is far different from the case of positive and negative charges, which are easily separated.) A current loop always produces a magnetic dipole—that is, a magnetic field that acts like a north pole and south pole pair. Since isolated north and south magnetic poles, called #strong[magnetic monopoles], are not observed, currents are used to explain all magnetic effects. If magnetic monopoles did exist, then we would have to modify this underlying connection that all magnetism is due to electrical current. There is no known reason that magnetic monopoles should not exist—they are simply never observed—and so searches at the subnuclear level continue. If they do #emph[not] exist, we would like to find out why not. If they #emph[do] exist, we would like to see evidence of them. #notebox("Note", rgb("#8a94a6"), rgb("#556666"), rgb("#f7f8fa"))[ #emph[Electric Currents and Magnetism] Electric current is the source of all magnetism. ] #figure(figph[Two atomic models that describe the relationship between the movement of electrons and magnetism.], alt: "Two atomic models that describe the relationship between the movement of electrons and magnetism.", caption: [(a) In the planetary model of the atom, an electron orbits a nucleus, forming a closed-current loop and producing a magnetic field with a north pole and a south pole. (b) Electrons have spin and can be crudely pictured as rotating charge, forming a current that produces a magnetic field with a north pole and a south pole. Neither the planetary model nor the image of a spinning electron is completely consistent with modern physics. However, they do provide a useful way of understanding phenomena.]) #notebox("Note", rgb("#8a94a6"), rgb("#556666"), rgb("#f7f8fa"))[ #emph[Magnets and Electromagnets] Explore the interactions between a compass and bar magnet. Discover how you can use a battery and wire to make a magnet! Can you make it a stronger magnet? Can you make the magnetic field reverse? #link("https://openstax.org/l/28elec_magnet")[Click to view content]. ] === Test Prep for AP Courses A bar magnet is oriented so that the north pole of the bar magnet points north. A compass needle is placed to the north of the bar magnet. In which direction does the north pole of the compass needle point? + North + East + South + West #solutionbox[ (a) ] Assume for simplicity that the Earth’s magnetic north pole is at the same location as its geographic north pole. If you are in an airplane flying due west along the equator, as you cross the prime meridian (0° longitude) facing west and look down at a compass you are carrying, you see that the compass needle is perpendicular to your direction of motion, and the north pole of the needle dipole points to your right. As you continue flying due west, describe how and why the orientation of the needle will (or will not) change. Describe how the magnetic domains in an unmagnetized iron rod will respond to the presence of a strong external magnetic field. + The domains will split into monopoles. + The domains will tend to align with the external field. + The domains will tend to orient themselves perpendicular to the external field. + The domains will tend to align so as to cancel out the external field. #solutionbox[ (b) ] Describe what steps must be undertaken in order to convert an unmagnetized iron rod into a permanently magnetized state. As part of your answer, explain what a magnetic domain is and how it responds to the steps described. Iron is ferromagnetic and lead is diamagnetic, which means its magnetic domains respond in the opposite direction of ferromagnets but many orders of magnitude more weakly. The two blocks are placed in a magnetic field that points to the right. Which of the following best represents the orientations of the dipoles when the field is present? #figure(table( columns: 3, align: left, inset: 6pt, table.header([], [Iron], [Lead]), [(a)], [#figure(figph[Multiple red arrows scattered and pointing in various directions on a white background, representing disorganization or random movement.], alt: "Multiple red arrows scattered and pointing in various directions on a white background, representing disorganization or random movement.", caption: none)], [#figure(figph[A white background displays multiple red arrows pointing randomly, illustrating a disordered or chaotic arrangement.], alt: "A white background displays multiple red arrows pointing randomly, illustrating a disordered or chaotic arrangement.", caption: none)], [(b)], [#figure(figph[A simple diagram displays nine red arrows arranged in three rows, each pointing uniformly towards the right against a white background.], alt: "A simple diagram displays nine red arrows arranged in three rows, each pointing uniformly towards the right against a white background.", caption: none)], [#figure(figph[Randomly oriented red arrows on a white field, depicting vector directions without a dominant trend.], alt: "Randomly oriented red arrows on a white field, depicting vector directions without a dominant trend.", caption: none)], [(c)], [#figure(figph[Randomly oriented red arrows on a white background, demonstrating a disordered state or non-uniform vector field.], alt: "Randomly oriented red arrows on a white background, demonstrating a disordered state or non-uniform vector field.", caption: none)], [#figure(figph[A white rectangular image with a black border contains nine red arrows, each pointing horizontally to the right. The arrows are arranged in three rows, with three arrows in each row, demonstrating a uniform direction.], alt: "A white rectangular image with a black border contains nine red arrows, each pointing horizontally to the right. The arrows are arranged in three rows, with three arrows in each row, demonstrating a uniform direction.", caption: none)], [(d)], [#figure(figph[A grid of nine red arrows all pointing to the right, arranged in three rows of three arrows each on a white background, suggesting uniform flow or direction.], alt: "A grid of nine red arrows all pointing to the right, arranged in three rows of three arrows each on a white background, suggesting uniform flow or direction.", caption: none)], [#figure(figph[Multiple red arrows point uniformly to the right within a rectangular frame, suggesting a singular direction or flow.], alt: "Multiple red arrows point uniformly to the right within a rectangular frame, suggesting a singular direction or flow.", caption: none)], )) #solutionbox[ (b) ] A weather vane is some sort of directional arrow parallel to the ground that may rotate freely in a horizontal plane. A typical weather vane has a large cross-sectional area perpendicular to the direction the arrow is pointing, like a “One Way” street sign. The purpose of the weather vane is to indicate the direction of the wind. As wind blows past the weather vane, it tends to orient the arrow in the same direction as the wind. Consider a weather vane’s response to a strong wind. Explain how this is both similar to and different from a magnetic domain’s response to an external magnetic field. How does each affect its surroundings? === Section Summary - Magnetic poles always occur in pairs of north and south—it is not possible to isolate north and south poles. - All magnetism is created by electric current. - Ferromagnetic materials, such as iron, are those that exhibit strong magnetic effects. - The atoms in ferromagnetic materials act like small magnets (due to currents within the atoms) and can be aligned, usually in millimeter-sized regions called domains. - Domains can grow and align on a larger scale, producing permanent magnets. Such a material is magnetized, or induced to be magnetic. - Above a material’s Curie temperature, thermal agitation destroys the alignment of atoms, and ferromagnetism disappears. - Electromagnets employ electric currents to make magnetic fields, often aided by induced fields in ferromagnetic materials.