Magnetism

Introduction

This chapter explores the fundamental principles of magnetism, including the properties of magnets, the relationship between electricity and magnetism, and the behavior of magnetic fields. Applications such as electric motors, galvanometers, and mass spectrometers are also discussed.

Magnets and Magnetic Fields

Magnetic Poles and Interactions

• Magnets have two ends called poles: north (N) and south (S).

• Like poles repel each other; unlike poles attract.

• If a magnet is cut in half, each piece forms a new magnet with both a north and a south pole.

Example: Cutting a bar magnet results in two smaller bar magnets, each with its own north and south poles.

Magnetic Field Lines

• Magnetic fields can be visualized using magnetic field lines, which always form closed loops from north to south outside the magnet and south to north inside.

• The Earth's magnetic field resembles that of a bar magnet. The geographic North Pole is actually a magnetic south pole, as it attracts the north end of a compass needle.

• A uniform magnetic field is constant in both magnitude and direction, such as the field between two wide, flat poles.

Electric Currents Produce Magnetic Fields

Oersted's Experiment and Right-Hand Rule

• Experiments show that an electric current produces a magnetic field around the conductor.

• The right-hand rule is used to determine the direction of the magnetic field: if you wrap your right hand around the wire with your thumb in the direction of the current, your fingers curl in the direction of the magnetic field lines.

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

Magnetic Force on a Current-Carrying Wire

• A magnet exerts a force on a current-carrying wire placed in its magnetic field.

• The direction of the force is given by the right-hand rule.

• The magnitude of the force is given by:

• I: current (A)

• L: length of wire in the field (m)

• B: magnetic field strength (T)

• θ: angle between current and magnetic field

Units: The SI unit of magnetic field (B) is the tesla (T), where . Another unit is the gauss (G): .

Force on Electric Charge Moving in a Magnetic Field

Lorentz Force

• A moving charge in a magnetic field experiences a force:

• q: charge (C)

• v: velocity (m/s)

• B: magnetic field (T)

• θ: angle between velocity and magnetic field

• The direction is given by the right-hand rule: point fingers in the direction of velocity, curl toward B, thumb points in the direction of force (for positive charges).

Example: A proton moving perpendicular to a magnetic field will experience a force perpendicular to both its velocity and the field, causing it to move in a circular path.

Circular Motion of Charged Particles

• If a charged particle moves perpendicular to a uniform magnetic field, it undergoes uniform circular motion.

• The radius of the path is given by:

• m: mass of the particle (kg)

• v: speed (m/s)

• q: charge (C)

• B: magnetic field (T)

Right-Hand Rules (Summary Table)

Magnetic Field Due to a Long Straight Wire

• The magnetic field at a distance r from a long, straight wire carrying current I is:

• μ₀: permeability of free space,

Force between Two Parallel Wires

• Two parallel wires carrying currents exert a force on each other due to their magnetic fields.

• The force per unit length between two wires separated by distance d is:

• Parallel currents attract; antiparallel currents repel.

Definition of the Ampere

• The ampere (A) is defined as the current that, when maintained in two straight parallel conductors 1 meter apart in vacuum, produces a force of per meter of length.

• The coulomb (C) is defined as the amount of charge transported by a current of 1 ampere in 1 second.

Solenoids and Electromagnets

• A solenoid is a long coil of wire; when current passes through, it creates a nearly uniform magnetic field inside.

• The field inside a solenoid is:

• N: number of turns

• I: current (A)

• ℓ: length of solenoid (m)

• Inserting an iron core increases the field strength, creating an electromagnet.

Ampère’s Law

• Ampère’s law relates the magnetic field around a closed loop to the total current passing through the loop:

• Useful for calculating fields in symmetric situations (e.g., long straight wires, solenoids).

Torque on a Current Loop; Magnetic Moment

• A current loop in a magnetic field experiences a torque:

• N: number of loops

• A: area of loop (m²)

• θ: angle between normal to the loop and B

• The magnetic dipole moment is

Applications: Galvanometers, Motors, Loudspeakers

• Galvanometer: Measures current by the torque on a current loop in a magnetic field.

• Electric motor: Converts electrical energy to mechanical energy using the torque on a current loop.

• Loudspeaker: Uses the force on a current-carrying wire in a magnetic field to produce sound vibrations.

Mass Spectrometer

• Measures the masses of atoms by analyzing the motion of charged particles in perpendicular electric and magnetic fields.

• For a particle to pass undeflected:

• In a magnetic field, the radius of curvature depends on the mass of the particle.

Ferromagnetism: Domains and Hysteresis

• Ferromagnetic materials (e.g., iron, nickel) can be strongly magnetized.

• They consist of domains, regions where the magnetic field is aligned.

• Unmagnetized materials have randomly oriented domains; applying an external field aligns them.

• Magnetization can persist (remanence) or be lost by shock or heat (demagnetization).

• The relationship between external and internal fields is complex and exhibits hysteresis—the lag between changes in magnetization and the applied field, shown in a hysteresis curve.

Summary Table: Key Equations