22: Magnetism
- Page ID
- 1462
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Magnetism is a class of physical phenomena that are mediated by magnetic fields. Electric currents and the magnetic moments of elementary particles give rise to a magnetic field, which acts on other currents and magnetic moments. Every material is influenced to some extent by a magnetic field.
- 22.0: Prelude to Magnetism
- Magnetism is used to explain atomic energy levels, cosmic rays, and charged particles trapped in the Van Allen belts. Once again, we will find all these disparate phenomena are linked by a small number of underlying physical principles.
- 22.1: Magnets
- Magnetism is a subject that includes the properties of magnets, the effect of the magnetic force on moving charges and currents, and the creation of magnetic fields by currents. There are two types of magnetic poles, called the north magnetic pole and south magnetic pole. North magnetic poles are those that are attracted toward the Earth’s geographic north pole. Like poles repel and unlike poles attract. Magnetic poles always occur in pairs of north and south.
- 22.2: Ferromagnets and Electromagnets
- 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.
- 22.3: Magnetic Fields and Magnetic Field Lines
- Magnetic fields can be pictorially represented by magnetic field lines, the properties of which are as follows: The field is tangent to the magnetic field line. Field strength is proportional to the line density. Field lines cannot cross. Field lines are continuous loops.
- 22.4: Magnetic Field Strength- Force on a Moving Charge in a Magnetic Field
- Magnetic fields exert a force on a moving charge q. The SI unit for magnetic field strength B is the tesla (T). The direction of the force on a moving charge is given by right hand rule 1: Point the thumb of the right hand in the direction of v, the fingers in the direction of B, and a perpendicular to the palm points in the direction of F. The force is perpendicular to the plane formed by \(mathbf{v}\) and \mathbf{B}.
- 22.5: Force on a Moving Charge in a Magnetic Field- Examples and Applications
- Magnetic force can supply centripetal force and cause a charged particle to move in a circular path of radius \[r = \frac{mv}{qB},\] where \(v\) is the component of the velocity perpendicular to \(B\) for a charged particle with mass \(m\) and charge \(q\).
- 22.6: The Hall Effect
- We have seen effects of a magnetic field on free-moving charges. The magnetic field also affects charges moving in a conductor. One result is the Hall effect, which has important implications and applications. The Hall effect is the creation of voltage εε\varepsilon, known as the Hall emf, across a current-carrying conductor by a magnetic field.
- 22.7: Magnetic Force on a Current-Carrying Conductor
- The magnetic force on current-carrying conductors is given by \[F = \pi B sin \theta,\] where \(\) is the current, \(l\) is the length of a straight conductor in a uniform magnetic field \(B\), and \(\theta\) is the angle between \(I\) and \(B\). The force follows RHR-1 with the thumb in the direction of \(I\).\
- 22.8: Torque on a Current Loop - Motors and Meters
- The torque \(\tau\) on a current-carrying loop of any shape in a uniform magnetic field. is \[\tau = NIABsin\theta,\] where \(N\) is the number of turns, \(I\) is the current, \(A\) is the area of the loop, \(B\) is the magnetic field strength, and \(\theta\) is the angle between the perpendicular to the loop and the magnetic field.
- 22.9: Magnetic Fields Produced by Currents- Ampere’s Law
- The strength of the magnetic field created by current in a long straight wire is given by \[B = \frac{\mu_{0}I}{2 \pi r} \left(long \quad straight \quad wire\right),\tag{22.10.1}\] where \(I\) is the current, \(r\) is the shortest distance to the wire, and the constant \(\mu_{0} = 4\pi \times 10^{-7} T \cdot m/a\) is the permeability of free space. The direction of the magnetic field created by a long straight wire is given by right hand rule 2 (RHR-2): Point the thumb of the right hand in the d
- 22.10: Magnetic Force between Two Parallel Conductors
- The force between two parallel currents \(I_{1}\) and \(I_{2}\) separated by a distance \(r\), has a magnitude per unit length given by \[\frac{F}{l} = \frac{\mu_{0}I_{1}I_{2}}{2\pi r}.\] The force is attractive if the currents are in the same direction, repulsive if they are in opposite directions.
- 22.11: More Applications of Magnetism
- Crossed (perpendicular) electric and magnetic fields act as a velocity filter, giving equal and opposite forces on any charge with velocity perpendicular to the fields and of magnitude \[v = \frac{E}{B}.\]
Thumbnail: Magnetic field of an ideal cylindrical magnet with its axis of symmetry inside the image plane. The magnetic field is represented by magnetic field lines, which show the direction of the field at different points. (CC-SA-BY-3.0; Geek3).