Chapter 20: Magnetism Study Notes

Chapter 20: Magnetism

Introduction

• This chapter discusses fundamental concepts related to magnetism including properties of magnets, magnetic fields, and interactions between electric currents and magnetic fields.

• It is structured into various sections covering different aspects of magnetism and is essential for understanding the principles of physics related to magnetic phenomena.

Contents Overview

• Topics discussed include:

  • Magnets and Magnetic Fields

  • Electric Currents Produce Magnetic Fields

  • Force on an Electric Current in a Magnetic Field; Definition of B

  • Force on Electric Charge Moving in a Magnetic Field

  • Magnetic Field Due to a Long Straight Wire

  • Force between Two Parallel Wires

  • Solenoids and Electromagnets

  • Ampère’s Law

  • Torque on a Current Loop; Magnetic Moment

  • Applications: Galvanometers, Motors, Loudspeakers

  • Mass Spectrometer

  • Ferromagnetism: Domains and Hysteresis

20-1: Magnets and Magnetic Fields

• Magnets possess two poles: North and South.

• Rule of Poles:

  • Like poles repel each other; unlike poles attract each other.

• Cutting a magnet in half does not produce a single north or south pole but results in two smaller magnets, each with its own north and south pole.

Magnet Properties and Experiments

• Experiment 4: Magnets can lift certain objects (e.g., paper clips) while some materials (copper, aluminum, glass, plastic) are unaffected.

• Experiment 5: A magnet near an electroscope does not affect the leaves unless a charged rod is nearby, which may cause minor polarization effects.

Summary of Experiments

• Conclusions drawn from experiments indicate:

  • Magnetism is distinct from electricity.

  • Magnetic poles share similar but not identical behaviors compared to electric charges.

20-2: Electric Currents Produce Magnetic Fields

• Electric current generates a magnetic field around conductors, which can be determined using the Right-Hand Rule.

• 2nd Right-Hand Rule: Demonstrates the direction of the produced magnetic field based on the direction of current.

20-3: Force on an Electric Current in a Magnetic Field; Definition of B

• A magnet affects a current-carrying wire. The force exerted on the wire is determined by its current, length, orientation, and the magnetic field present.

• Definition of magnetic field: B (Tesla)

• Unit: $1 T = 1\frac{N}{A \cdot m}$

• Alternative unit: Gauss (G) - $1 G = 10^{-4} T$

20-4: Force on Electric Charge Moving in a Magnetic Field

• A magnetic field exerts a force on a charge that is moving.

• Key observations:

  • No magnetic force exists when the charged particle is stationary.

  • No magnetic force if the particle moves parallel to the magnetic field.

  • Maximum force occurs when the angle (α) between the particle's velocity and the magnetic field is $90^{\circ}$.

• If the charged particle moves perpendicularly to a magnetic field, it follows a circular path due to the continuous magnetic force acting as a centripetal force.

• Magnetic force (for perpendicular motion):

  $F = qvB$

• Equated with circular motion force, $F = \frac{mv^2}{r}$ leading to the gyroradius: $r = \frac{mv}{qB}$

20-5: Magnetic Field Due to a Long Straight Wire

• The magnetic field (B) from a straight wire is inversely proportional to the distance from that wire.

• Relationship: $B = \frac{\mu_0 I}{2\pi r}$

  • Field strength decreases with distance.

• Permeability of Free Space: $\mu_0 = 4\pi \times 10^{-7} T\cdot m/A$

20-6: Force between Two Parallel Wires

• Parallel wires carrying current exert forces on each other; this force depends on the direction of the currents.

• Rule: Parallel currents attract, antiparallel currents repel.

• Force per unit length relationship for parallel wires formula:

  $F<em>{12} = \frac{\mu</em>0}{2\pi r} I<em>1 I</em>2$

20-7: Solenoids and Electromagnets

• A solenoid is a coil of wire that produces a magnetic field when electric current passes through it.

• A tightly wound solenoid exhibits a nearly uniform interior magnetic field.

• Inserting iron into the solenoid increases the magnetic field significantly, thus functioning as an electromagnet with numerous applications.

20-8: Ampère’s Law

• Ampère’s law connects the magnetic field within a closed loop to the total current enclosed by that loop:

• Formula:

  $B = \frac{\mu<em>0}{2}I</em>{enc}$

• Useful for analyzing systems with high symmetry.

20-9: Torque on a Current Loop; Magnetic Moment

• The interaction of a current loop in a magnetic field can cause a torque, which causes the loop to rotate.

• Torque Magnitude Relation:

  • $\tau = M \times B$ where M is the magnetic moment defined as $M = NIA$

20-10: Applications: Galvanometers, Motors, Loudspeakers

• Galvanometers utilize induced torque to measure electric current.

• Electric Motors: Transform electrical energy to mechanical energy through the torque on current loops.

• Loudspeakers: Utilize forces on current wires within magnetic fields to convert electrical signals into sound.

20-11: Mass Spectrometer

• A mass spectrometer is employed to measure the masses of atoms.

• Charged particles traversing perpendicular electric and magnetic fields experience select speeds without deflection, a phenomenon termed velocity selection.

20-12: Ferromagnetism: Domains and Hysteresis

• Ferromagnetic materials (e.g., iron, nickel) can become strongly magnetized due to the alignment of internal domains, which can be either randomly oriented (unmagnetized) or aligned (magnetized).

• The hysteresis curve illustrates the relation between an external magnetic field and an internal magnetic field within a ferromagnet, showing how magnetization levels change with varying external influences.