Principles of Physics II

🎢Principles of Physics II Unit 6 – Magnetism and Magnetic Fields

Magnetism and magnetic fields are fundamental forces in nature, arising from moving electric charges and intrinsic properties of subatomic particles. These fields exert forces on moving charges and other magnetic fields, playing a crucial role in various natural phenomena and technological applications. Understanding magnetism is essential for grasping concepts in electromagnetism, a cornerstone of modern physics. From Earth's magnetic field to advanced technologies like MRI machines and particle accelerators, magnetic fields shape our world and drive scientific progress.

Fundamental Concepts of Magnetism

  • Magnetism arises from the motion of electric charges and the intrinsic magnetic moments of subatomic particles
  • Magnetic fields exert forces on moving charges and other magnetic fields
  • Magnetic poles always occur in pairs (north and south) and cannot be separated like electric charges
  • Magnetic field lines represent the direction and strength of the magnetic field at any point in space
  • Magnetic flux (ΦB\Phi_B) measures the amount of magnetic field passing through a surface
    • Calculated using the equation ΦB=BdA\Phi_B = \int \vec{B} \cdot d\vec{A}
  • Gauss's law for magnetism states that the net magnetic flux through any closed surface is always zero
  • Ampère's law relates the magnetic field around a closed loop to the electric current passing through the loop
    • Expressed as Bdl=μ0Ienc\oint \vec{B} \cdot d\vec{l} = \mu_0 I_{enc}, where μ0\mu_0 is the permeability of free space and IencI_{enc} is the enclosed current

Magnetic Fields and Their Properties

  • Magnetic fields are vector fields represented by the symbol B\vec{B} and measured in teslas (T) or gauss (G)
  • The direction of a magnetic field is defined as the direction a north pole of a compass needle points when placed in the field
  • Magnetic field lines never cross each other and form closed loops
  • The strength of a magnetic field decreases with distance from the source
  • Magnetic fields can be represented by field lines, with the density of lines indicating the strength of the field
  • The Earth's magnetic field resembles that of a large bar magnet, with field lines extending from the south magnetic pole to the north magnetic pole
    • The Earth's magnetic poles do not coincide with its geographic poles
  • Magnetic fields can be uniform (constant in magnitude and direction) or non-uniform (varying in magnitude and/or direction)

Sources of Magnetic Fields

  • Moving electric charges, such as electric currents, generate magnetic fields
  • Permanent magnets produce magnetic fields due to the alignment of magnetic moments of atoms within the material
  • Electromagnets generate magnetic fields when an electric current flows through a coil of wire
    • The strength of the magnetic field can be increased by increasing the number of turns in the coil or the current flowing through it
  • The Biot-Savart law describes the magnetic field generated by a current-carrying wire
    • dB=μ04πIdl×r^r2d\vec{B} = \frac{\mu_0}{4\pi} \frac{I d\vec{l} \times \hat{r}}{r^2}, where II is the current, dld\vec{l} is a small segment of the wire, and r^\hat{r} is the unit vector pointing from the wire segment to the point of interest
  • Ampère's law relates the magnetic field around a closed loop to the electric current passing through the loop
  • Solenoids and toroidal coils produce strong, uniform magnetic fields inside the coil when a current is passed through them
  • The magnetic field inside a solenoid is given by B=μ0nIB = \mu_0 n I, where nn is the number of turns per unit length and II is the current

Magnetic Forces on Moving Charges

  • A moving charged particle experiences a force when placed in a magnetic field
  • The magnetic force on a moving charge is perpendicular to both the magnetic field and the velocity of the charge
    • Described by the equation F=qv×B\vec{F} = q\vec{v} \times \vec{B}, where qq is the charge, v\vec{v} is the velocity, and B\vec{B} is the magnetic field
  • The direction of the magnetic force is determined by the right-hand rule
  • The magnitude of the magnetic force depends on the charge, velocity, magnetic field strength, and the angle between the velocity and magnetic field vectors
  • Charged particles moving parallel to a magnetic field experience no force, while those moving perpendicular to the field experience the maximum force
  • Magnetic fields can be used to guide and manipulate charged particle beams in applications such as cathode ray tubes (CRTs) and particle accelerators

Magnetic Forces on Current-Carrying Conductors

  • A current-carrying wire placed in a magnetic field experiences a force
  • The magnetic force on a current-carrying conductor is perpendicular to both the magnetic field and the direction of the current
    • Given by the equation F=IL×B\vec{F} = I\vec{L} \times \vec{B}, where II is the current, L\vec{L} is the length vector of the conductor, and B\vec{B} is the magnetic field
  • The direction of the force is determined by the right-hand rule
  • The magnitude of the force depends on the current, length of the conductor, magnetic field strength, and the angle between the current and magnetic field vectors
  • Parallel conductors carrying currents in the same direction attract each other, while those carrying currents in opposite directions repel each other
  • Magnetic forces on current-carrying conductors are the basis for the operation of electric motors and loudspeakers
    • In an electric motor, the magnetic force on a current-carrying coil causes it to rotate, converting electrical energy into mechanical energy

Applications of Magnetism in Technology

  • Magnetic resonance imaging (MRI) uses strong magnetic fields and radio waves to create detailed images of the human body
    • Protons in the body's tissues align with the applied magnetic field and absorb and emit radio waves, providing information about the tissue structure
  • Magnetic levitation (maglev) trains use powerful electromagnets to lift and propel the train above a guideway, reducing friction and allowing high-speed travel
  • Hard disk drives (HDDs) store digital data using magnetic recording on a rapidly rotating disk coated with a magnetic material
    • Read/write heads use magnetic fields to read and write data on the disk surface
  • Transformers use magnetic coupling between coils to step up or step down alternating current (AC) voltages for efficient power transmission and distribution
  • Electromagnetic locks use an electromagnet to secure a door when an electric current is applied, and release the door when the current is removed
  • Magnetometers measure the strength and direction of magnetic fields and are used in applications such as navigation, geophysical surveys, and space exploration
  • Particle accelerators use magnetic fields to guide and accelerate charged particles to high energies for research in physics, chemistry, and materials science

Electromagnetic Induction

  • Electromagnetic induction is the production of an electromotive force (emf) in a conductor by a changing magnetic flux
  • Faraday's law of induction states that the induced emf in a closed loop is equal to the negative rate of change of the magnetic flux through the loop
    • Expressed as E=dΦBdt\mathcal{E} = -\frac{d\Phi_B}{dt}, where E\mathcal{E} is the induced emf and ΦB\Phi_B is the magnetic flux
  • Lenz's law states that the direction of the induced emf is such that it opposes the change in magnetic flux that produced it
  • Motional emf is induced when a conductor moves through a magnetic field, as described by the equation E=Blv\mathcal{E} = Blv, where BB is the magnetic field strength, ll is the length of the conductor, and vv is the velocity of the conductor
  • Generators and alternators use electromagnetic induction to convert mechanical energy into electrical energy
    • A coil of wire rotates in a magnetic field, inducing an alternating current in the coil
  • Transformers use electromagnetic induction to step up or step down AC voltages
    • Two coils are wound around a common iron core, and a changing current in the primary coil induces a voltage in the secondary coil
  • Eddy currents are induced currents in conducting materials that arise due to changing magnetic fields
    • These currents can cause heating and energy losses in transformers and other devices

Magnetic Materials and Domains

  • Magnetic materials can be classified as diamagnetic, paramagnetic, or ferromagnetic based on their response to external magnetic fields
  • Diamagnetic materials have no unpaired electrons and are weakly repelled by magnetic fields (bismuth, copper, water)
  • Paramagnetic materials have unpaired electrons and are weakly attracted to magnetic fields (aluminum, platinum, oxygen)
  • Ferromagnetic materials have strong magnetic properties due to the alignment of magnetic moments in magnetic domains (iron, nickel, cobalt)
    • Magnetic domains are regions within a ferromagnetic material where the magnetic moments of atoms are aligned in the same direction
  • The alignment of magnetic domains can be influenced by external magnetic fields, temperature, and mechanical stress
  • Ferromagnetic materials can be magnetized by placing them in a strong external magnetic field, causing the magnetic domains to align
  • The magnetic properties of ferromagnetic materials depend on their composition, microstructure, and temperature
    • Above the Curie temperature, ferromagnetic materials become paramagnetic as thermal energy disrupts the alignment of magnetic moments
  • Soft magnetic materials (iron) are easily magnetized and demagnetized, while hard magnetic materials (neodymium) retain their magnetization and are used to create permanent magnets
  • Hysteresis is the dependence of a ferromagnetic material's magnetization on its magnetic history
    • The hysteresis loop represents the relationship between the applied magnetic field and the resulting magnetization of the material


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AP® and SAT® are trademarks registered by the College Board, which is not affiliated with, and does not endorse this website.
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