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Magnetism Module Overview

Acknowledgments This presentation is based on and includes content derived from the following OER resource: College Physics An OpenStax book used for this course may be downloaded for free at: https://openstax.org/details/books/college-physics

Magnets All magnets attract iron and have two poles, called north and south for their attraction to the North and South Poles of the Earth. Note, though, that the Geographic North Pole is actually near the South Magnetic Pole. Like magnetic poles repel and unlike magnetic poles attract. No magnet can be split into a single pole. Splitting a magnet results in two magnets, each with north and south poles. (College Physics. OpenStax. Fig. 22.5.)

Ferromagnets Some materials like iron, called ferromagnetic materials, exhibit strong magnetic effects. When an unmagnetized ferromagnetic material is brought near a magnetic field, the material can be induced to become a permanent magnet by realigning microscopic domains that behave like bar magnets. Conversely, striking or heating the material can destroy the magnetic alignment. (College Physics. OpenStax. Fig. 22.8.)

Electromagnets Electrical currents were first observed to cause magnetic effects in the early 19th century, when Hans Christian Oersted observed a compass needle deflected by a current-carrying wire. Electromagnetism is the use of current to create magnets, called electromagnets. Combining electromagnets with ferromagnetic materials can enhance the magnetic field. (College Physics. OpenStax. Fig. 22.10.)

The Source of All Magnetism Electric current is the source of all magnetism. Electromagnets create magnetism with macroscopic currents. Ferromagnets create magnetism with submicroscopic currents on the atomic scale. The angular momentum of the electron around the atom creates electric current that produces magnetic materials. (College Physics. OpenStax. Fig. 22.13.)

Magnetic Fields and Field Lines The magnetic force can be described by the magnetic field, or 𝑩-field. The magnetic field is visualized by drawing magnetic field lines, which are closed loops that emanate from north magnetic poles and terminate on south magnetic poles. The direction of the field is tangent to the field lines and proportional to the closeness of the lines. Field lines are continuous and never cross. (College Physics. OpenStax. Figs. 22.15, 22.16.)

Magnetic Field Strength The Lorentz force on a moving charge 𝑞 is given in the terms of its velocity 𝑣 and field strength 𝐵 by 𝐹=𝑞𝑣𝐵sin𝜃, where 𝜃 is the angle between the velocity and field vectors. The SI unit of magnetic field is the tesla (T), defined as 1 T=1 N A∙m . The direction of the force is perpendicular to the velocity and field, as given by right-hand rule-1 shown in the diagram. (College Physics. OpenStax. Fig. 22.17.)

Force On a Moving Charge in a Magnetic Field For a charge with velocity perpendicular to a magnetic field, the magnetic force acts as a centripetal force. Newton’s second law gives 𝑞𝑣𝐵= 𝑚 𝑣 2 𝑟 , which can be solved to give a radius of curvature, 𝑟= 𝑚𝑣 𝑞𝐵 . This behavior can be observed in charged particles in the Earth’s atmosphere, and finds practical uses in particle accelerators and fusion reactors. (College Physics. OpenStax. Fig. 22.20.)

The Hall Effect The Hall effect is the creation of a voltage, called the Hall emf, across a current-carrying conductor in a magnetic field. The magnetic force on the moving charges is balanced by the electric field that builds up, given by 𝑞𝐸=𝑞𝑣𝐵. The Hall emf is related to the electric field by 𝐸= ℇ 𝑙 for a conductor with width 𝑙. The Hall emf is given by ℇ=𝐵𝑙𝑣. (College Physics. OpenStax. Fig. 22.28.)

Magnetic Force on a Current-Carrying Conductor Because charges are typically bound to a conductor, the magnetic force on the moving charges results in a force on the conductor. The force on a wire of length 𝑙 with current 𝐼 is given by 𝐹=𝐼𝑙𝐵sin𝜃, where 𝐵 is the magnetic field and 𝜃 is the angle between the current and field. One application of this force is to pump conductive fluids with no moving parts using only current and the magnetic force. (College Physics. OpenStax. Figs. 22.30.)

Torque on a Current Loop For a rectangular loop with 𝑁 turns and area 𝐴, the magnetic force creates a torque on the loop given by 𝜏=𝑁𝐼𝐴𝐵sin𝜃, where 𝜃 is the angle between the magnetic field and the normal to the loop. This torque can be used as a galvanometer or used in conjunction with an alternating current to create a motor that converts electrical energy into mechanical energy. (College Physics. OpenStax. Figs. 22.35.)

Magnetic Field from a Long, Straight Wire The magnetic field produced by a long, straight wire is proportional to the current 𝐼 flowing through the wire, according to the expression 𝐵= 𝜇 0 𝐼 2𝜋𝑟 , where 𝜇 0 =4π× 10 −7 T∙m/A is the permeability of free space. The direction of the field is given by right-hand rule-2, shown in the diagram. The thumb points in the direction of the current and the fingers wrap around the wire in the direction of the magnetic field. (College Physics. OpenStax. Fig. 22.38.)

Ampere’s Law Any current-carrying wire produces a magnetic field. The field can be found by breaking the wire into short, approximately straight wire segments and adding up their contributions to the total field. The mathematical relation used to do the sum involves integral calculus and is called the Biot-Savart law. Summed over an arbitrary current distribution, the Biot-Savart law gives rise to Ampere’s law, which relates magnetic fields and currents and is one of four equations, collectively called Maxwell’s equations, that describe all electromagnetic phenomena.

Magnetic Field of a Current-Carrying Loop At the center of a loop of current-carrying wire, the magnetic field due to the loop is given by 𝐵= 𝜇 0 𝐼 2𝑅 , where 𝑅 is the radius of the loop. For a coil with 𝑁 loops, the magnetic field is increased to 𝐵= 𝑁𝜇 0 𝐼 2𝑅 . Larger loops result in a smaller field at the center because the current is farther away. (College Physics. OpenStax. Fig. 22.39.)

Magnetic Field of a Solenoid A solenoid is a long coil of wire. The magnetic field outside the solenoid is nearly zero, but the field inside the coil is approximately uniform near the center of the coil, given by 𝐵= 𝜇 0 𝑛𝐼, where 𝑛 is the density of the loops per unit length, 𝑛=𝑁/𝑙. Fusion reactors use a large solenoid bent into a circle, called a toroid, to produce strong magnetic fields where particles can collide and undergo fusion. (College Physics. OpenStax. Fig. 22.40.)

Magnetic Force Between Parallel Conductors A wire in a magnetic field produces a magnetic field, and a wire in a magnetic field experiences a magnetic force. This causes two nearby current-carrying wires to exert a magnetic force on one another, 𝐹 2 = 𝐼 2 𝑙 𝐵 1 . The force per unit length on each wire is proportional to their currents and inversely proportional to the distance between them, 𝐹 𝑙 = 𝜇 0 𝐼 1 𝐼 2 2𝜋𝑟 . (College Physics. OpenStax. Fig. 22.42.)

Mass Spectrometry In a mass spectrometer, a detector measures the radius of curvature of charged particles in a magnetic field to determine their masses. The radius of curvature of the path is given by 𝑟= 𝑚𝑣 𝑞𝐵 . The magnetic field has a known value and a velocity selector using electric and magnetic fields can be used to only accept particles at a particular velocity, 𝑣= 𝐸 𝐵 . (College Physics. OpenStax. Fig. 22.43.)

Cathode Ray Tubes The first televisions and computer monitors, along with x-ray machines and some particle accelerators, all use a version of the electron gun, also called a cathode ray tube (CRT). The CRT uses a strong electric field to accelerate electrons and magnetic fields are used to steer the electrons to the desired locations. (College Physics. OpenStax. Fig. 22.44.)

Magnetic Resonance Imaging Magnetic resonance imaging (MRI) is a non-invasive technique for imaging the inside of the body without the hazards of other methods. It works by creating a strong magnetic field using superconducting magnets. The magnetic field exerts a torque on atomic nuclei that causes them to align either parallel or antiparallel to the field. An external radio-wave signal is then used to induce the nuclei to flip from one orientation to the other, and the absorption and reemission of the radio waves can be precisely measured. This process allows the density, function, and location of different tissues in the body to be mapped with a high degree of precision. Unfortunately, MRI is both expensive and less useful than x-rays for measuring some tissues, so x-rays and MRI complement one another.

Other Medical Uses of Magnetic Fields Magnetic fields can be used to measure the magnetic activity of the heart via a magnetocardiogram, and the brain via a magnetoencephalogram. However, these technologies are currently difficult and immature, making them much less common than their electrical counterparts. There is a growing market for magnetic cures for various physical ailments, using magnets placed on various parts of the body. However, there is currently no clinical basis for claims that such cures work, and no mechanism is known that would make these cures effective.

How to Study this Module Read the syllabus or schedule of assignments regularly. Understand key terms; look up and define all unfamiliar words and terms. Take notes on your readings, assigned media, and lectures. As appropriate, work all questions and/or problems assigned and as many additional questions and/or problems as possible. Discuss topics with classmates. Frequently review your notes. Make flow charts and outlines from your notes to help you study for assessments. Complete all course assessments.

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