Magnetism and Magnetic Fields: Principles and Applications

Ch 24: Magnetism

Introduction to Magnetism

Magnetism is a fundamental physical phenomenon arising from the motion of electric charges, resulting in attractive and repulsive forces between objects. Magnets exhibit two distinct poles: north and south. Like magnetic poles repel each other, while unlike poles attract.

• Magnetic Poles: The north pole seeks the Earth's north, and the south pole is its opposite.

• Demonstrations: Magnets on swivels show attraction and repulsion; both ends attract steel objects.

Magnetic Field Visualization

The magnetic field (B) is a vector field surrounding magnets and current-carrying wires. It can be visualized using iron filings or arrows, which align along the field lines.

• Field Lines: Emerge from the north pole and enter the south pole outside the magnet; inside, they run from south to north.

• Vector Nature: All vector rules apply to magnetic fields.

• Demo: Magnet and array of arrows; magnet with iron filings.

Magnetic Monopoles

Unlike electric charges, magnetic monopoles do not exist in nature. Every magnet has both a north and south pole, even when broken.

• Demo: Broken magnet on array of arrows shows new poles form at the break.

Earth's Magnetic Field

The Earth acts as a giant magnet, with its magnetic south pole near the geographic north pole. The magnetic field extends into space and affects compass navigation.

• Geographic vs. Magnetic Poles: The south pole of Earth's magnet is not at the north geographic pole.

• Field Mapping: The position of the magnetic pole changes over time.

Electromagnetism: Interaction of Charges and Magnetic Fields

Magnetic fields interact with electric charges, but only when the charges are in motion. This interaction is called electromagnetism.

• Key Quantities: Magnitude of charge and magnetic field.

• Testing for Charge: Use charged rods and Crooks tube with magnets.

Force on Moving Charges in Magnetic Fields

A moving charge in a magnetic field experiences a force. The magnitude and direction depend on the velocity of the charge and the orientation of the field.

• Perpendicular Motion: $F = qvB$ (for v ⟂ B)

• General Case: $F = qvB\sin\theta$ (θ is the angle between v and B)

• Units of B: $B = \frac{F}{qv}$, measured in tesla (T); 1 G = 0.0001 T

Typical Magnetic Fields

Physical System	Magnetic Field (G)
Earth	0.50
Bar magnet	100
Sunspots	1000
Low-field MRI	2000
High-field MRI	15,000
Strongest manmade magnet	6 × 105
Magnetar (neutron star)	1015

Direction of Magnetic Force: Right Hand Rule and Cross Product

The direction of the magnetic force is given by the right hand rule and the vector cross product:

• Vector Form: $\vec{F} = q(\vec{v} \times \vec{B})$

• Right Hand Rule: Fingers point in direction of velocity (v), curl toward B, thumb points in direction of force (F) for positive charge; opposite for negative charge.

• Notation: '×' for into the page, '•' for out of the page.

Motion of Charged Particles in Magnetic Fields

Charged particles moving in magnetic fields follow circular or helical paths, depending on the angle of entry.

• Perpendicular Entry: Circular motion.

• Angled Entry: Helical motion.

• Application: Northern lights are caused by charged solar particles spiraling into Earth's atmosphere, exciting molecules and emitting light.

Source of Magnetic Fields

Magnetic fields are produced by moving charges, such as electric currents. The strength and direction of the field depend on the configuration of the current.

• Long, Straight Wire: $B = \frac{\mu_0 I}{2\pi d}$, where $\mu_0 = 4\pi \times 10^{-7} \text{T} \cdot \text{m} / \text{A}$

• Circular Loop: $B = \frac{\mu_0 I}{2r}$ at the center

• Solenoid: $B = \mu_0 n I$ where $n = N/L$ is the number of turns per meter

Magnetic Materials and Domains

Some materials are magnetic due to the atomic structure and electron spin. In most atoms, electron spins pair and cancel out, but in magnetic materials, unpaired spins create net magnetic moments and domains.

• Electron Spin: Each electron has a magnetic moment.

• Magnetic Domains: Groups of atoms with aligned magnetic moments.

• Example: Aluminum is non-magnetic due to paired spins; ferromagnetic materials have unpaired spins.

Magnetic Forces on Current-Carrying Wires

Current-carrying wires in magnetic fields experience forces due to the motion of charges.

• Force on Wire: $F = I L B \sin\theta$

• Direction: Use right hand rule; fingers along current, curl toward B, thumb points to force.

• Applications: Deflection of wires, DC motors, and electromagnetic devices.

Magnetic Force Between Parallel Wires

Parallel currents attract, anti-parallel currents repel, due to the magnetic fields generated by each wire.

• Demo: Jumping wire, rolling rod, parallel and anti-parallel wires.

Torque on a Current-Carrying Loop

A current loop in a magnetic field experiences a torque, which is the basis for electric motors.

• Torque Equation: $\tau = IAB\sin\theta$ where A is the area of the loop

• Motor Principle: To keep the loop rotating, the current must be reversed every 180 degrees (commutator).

Technological Applications

Magnetism is used in many technologies, including TV screens, computer monitors, and electric motors.

• Demo: Magnet near a TV screen.

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