Chapter 22: Magnetism – Study Notes

Magnetism

Introduction to Magnetism

Magnetism is a fundamental aspect of physics, describing the forces and fields associated with magnets and moving electric charges. This chapter explores the properties of magnetic fields, the forces they exert, and their interactions with matter and electric currents.

The Magnetic Field

Properties of Magnets

• Poles: Every magnet has two poles: north and south. Like poles repel, and opposite poles attract.

• Indivisibility of Poles: Breaking a magnet results in two smaller magnets, each with a north and south pole.

Magnetic Field Lines

• Magnetic fields are visualized using magnetic field lines, which show the direction and strength of the field.

• Field lines exit from the north pole and enter the south pole.

• Field lines never cross each other.

• Iron filings can be used to reveal the pattern of magnetic field lines around a magnet.

Earth’s Magnetic Field

• The Earth acts like a giant bar magnet, with its magnetic field resembling that of a bar magnet.

• The geographic north pole is actually a magnetic south pole, as it attracts the north pole of a compass needle.

The Magnetic Force on Moving Charges

Definition and Magnitude

• The magnetic force on a moving charge is used to define the magnetic field B.

• SI unit of force: newton (N).

The magnitude of the force on a charge q moving with velocity v in a magnetic field B is:

$F = |q|vB\sin\theta$

Direction of the Magnetic Force

• The direction is given by the right-hand rule for a positive charge: point your fingers in the direction of velocity, curl them toward the magnetic field, and your thumb points in the direction of the force.

• For a negative charge, the force is in the opposite direction.

• This relationship is expressed as a vector cross product:

$\vec{F} = q\vec{v} \times \vec{B}$

The Motion of Charged Particles in a Magnetic Field

Nature of the Motion

• In a magnetic field, the force on a charged particle is always perpendicular to its velocity, causing circular motion.

• The speed of the particle remains constant because the magnetic force does no work.

Radius of Circular Path

• For a particle of mass m and charge q moving at speed v in a magnetic field B:

$r = \frac{mv}{|q|B}$

Applications: Mass Spectrometer

• Devices like mass spectrometers use this principle to separate ions of different mass and charge by their circular paths.

Helical Motion

• If the velocity of the particle is at an angle to the magnetic field, the particle moves in a helical (spiral) path.

• The component of velocity parallel to the field remains unchanged.

The Magnetic Force Exerted on a Current-Carrying Wire

• A current-carrying wire in a magnetic field experiences a force.

• The force on a segment of wire of length L carrying current I is:

$\vec{F} = I\vec{L} \times \vec{B}$

Loops of Current and Magnetic Torque

Torque on a Current Loop

• Forces on opposite sides of a current loop in a magnetic field create a torque.

• The torque \tau on a rectangular loop of area A is:

$\tau = IAB\sin\theta$

• If the loop has N turns:

$\tau = N I A B \sin\theta$

• This principle is used in devices like galvanometers.

Electric Currents, Magnetic Fields, and Ampère’s Law

Magnetic Field Due to a Current

• Electric currents produce magnetic fields that form circles around the wire.

• The direction is given by the right-hand rule: thumb in the direction of current, fingers curl in the direction of the field.

Magnitude of the Magnetic Field

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

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

• SI unit: tesla (T).

Ampère’s Law

• Relates the integrated magnetic field around a closed loop to the current passing through the loop:

$\oint \vec{B} \cdot d\vec{l} = \mu_0 I_{enc}$

Force Between Parallel Wires

• Parallel current-carrying wires exert forces on each other due to their magnetic fields.

Current Loops and Solenoids

Magnetic Field of a Loop

• The field at the center of a current loop is similar to that of a bar magnet.

Solenoids

• A solenoid is a coil of wire in the shape of a cylinder.

• The magnetic field inside a long solenoid is:

$B = \mu_0 n I$

• where n is the number of turns per unit length.

Magnetism in Matter

Atomic Origins of Magnetism

• Electrons in atoms create magnetic fields through their motion.

• In most materials, these fields cancel out, but in some, they align to produce a net field.

Ferromagnetism

• Materials with strong, aligned atomic magnetic fields are called ferromagnetic.

• Ferromagnets have domains—regions with aligned magnetic fields.

• Permanent magnets are ferromagnetic and can retain magnetization.

Paramagnetism and Diamagnetism

• Paramagnetic materials align weakly with an external field, but lose alignment when the field is removed.

• Diamagnetic materials develop a weak magnetic field in the opposite direction to an applied field; this effect is present in all materials.

Summary Table: Types of Magnetic Materials

Type	Behavior in Magnetic Field	Example
Ferromagnetic	Strong, permanent alignment; can retain magnetization	Iron, Nickel, Cobalt
Paramagnetic	Weak, temporary alignment with field	Aluminum, Platinum
Diamagnetic	Weak, induced field opposite to applied field	Copper, Bismuth

Key Equations

• Magnetic force on a charge: $\vec{F} = q\vec{v} \times \vec{B}$

• Radius of circular motion: $r = \frac{mv}{|q|B}$

• Force on a current-carrying wire: $\vec{F} = I\vec{L} \times \vec{B}$

• Torque on a current loop: $\tau = N I A B \sin\theta$

• Magnetic field around a wire: $B = \frac{\mu_0 I}{2\pi r}$

• Ampère’s Law: $\oint \vec{B} \cdot d\vec{l} = \mu_0 I_{enc}$

• Magnetic field in a solenoid: $B = \mu_0 n I$