Magnetism

The Invisible Force

Lesson Plan

  • What is Magnetism?
  • Magnetic Poles & Fields
  • Electromagnetism
  • Magnetic Force on Charges (Lorentz Force)
  • Magnetic Induction
  • Maxwell's Equations
  • Applications & Problems
  • Interactive Quiz

What is Magnetism?

Magnetism is a fundamental force of nature produced by moving electric charges. It is responsible for the forces of attraction or repulsion between objects.

Simple Examples

A fridge magnet sticking to your refrigerator and a compass needle pointing North.

Magnetic Poles

Every magnet has two ends called poles: a North pole (N) and a South pole (S).

N S

Bar Magnet

S N

Another example

The Rule of Magnetic Poles

This is one of the most fundamental rules of magnetism:

  • Like poles repel: North repels North, and South repels South.
  • Unlike poles attract: North attracts South.

Interactive: Pole Interaction

Observe the behavior of two magnets as you change their polarity.

N S
N S

The Magnetic Field

A magnetic field is the area of magnetic force around a magnet. It is an invisible field that can exert a force on other magnetic materials.

Magnetic Field Lines

We visualize magnetic fields using magnetic field lines. These lines:

  • Always point away from the North pole.
  • Always point towards the South pole.
  • Never cross each other.
  • The density of the lines indicates the strength of the field.

Simulation: Magnetic Field Lines

Watch how iron filings (particles) trace out the invisible field lines around a bar magnet.

Earth: A Giant Magnet

The Earth has its own magnetic field, generated by molten iron in its core. This field protects us from harmful solar radiation, creating a protective "shield" called the magnetosphere. Interact with the 3D model below.

Interactive 3D Model

Click and drag to rotate.

Scroll to zoom in/out.

What Causes Magnetism?

Magnetism is fundamentally caused by moving electric charges. In magnetic materials, groups of atoms form magnetic domains that act like tiny magnets.

Unmagnetized

N N N N N

Domains are randomly oriented.

Magnetized

N N N N N

Domains are aligned, creating a strong field.

Ferromagnetic Materials

These are materials that can be strongly magnetized. They have a high concentration of aligned magnetic domains. Examples include:

  • Iron
  • Nickel
  • Cobalt

Electromagnetism

The link between electricity and magnetism. When electric charge flows (a current), it creates a magnetic field. This is the basis of electromagnets.

Oersted's Discovery

In 1820, Hans Christian Ørsted discovered that a compass needle deflects when placed near a current-carrying wire, proving that electricity and magnetism are related.

The Magnetic Field of a Wire

A current-carrying wire produces a circular magnetic field around it. The strength decreases with distance from the wire.

Right-Hand Rule (for a wire)

To determine the direction of the magnetic field around a wire, imagine grasping the wire with your right hand:

  • Point your thumb in the direction of the current ($I$).
  • Your curled fingers will point in the direction of the magnetic field ($B$).

Magnetic Field Strength

For a long, straight current-carrying wire, the magnetic field strength ($B$) is given by:

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

  • $B$ is the magnetic field strength (Tesla, T).
  • $\mu_0$ is the permeability of free space ($4\pi \times 10^{-7} \, \text{T} \cdot \text{m/A}$).
  • $I$ is the current (Amperes, A).
  • $r$ is the distance from the wire (meters, m).

Practice Problem 1

A long wire carries a current of $5 \, \text{A}$. What is the magnetic field strength at a distance of $0.1 \, \text{m}$ from the wire?

Hint: Use the formula $B = \frac{\mu_0 I}{2\pi r}$.

Solution to Problem 1

Using the formula:

$$B = \frac{(4\pi \times 10^{-7} \, \text{T} \cdot \text{m/A}) \times 5 \, \text{A}}{2\pi \times 0.1 \, \text{m}}$$

$$B = \frac{20\pi \times 10^{-7}}{0.2\pi} = 1.0 \times 10^{-5} \, \text{T}$$

Magnetic Force on a Moving Charge

A magnetic field exerts a force on a moving electric charge. This force is known as the Lorentz force.

The Lorentz Force Formula

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

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

  • $F$ is the magnetic force (Newtons, N).
  • $q$ is the magnitude of the charge (Coulombs, C).
  • $v$ is the speed of the charge (m/s).
  • $B$ is the magnetic field strength (Tesla, T).
  • $\theta$ is the angle between the velocity vector and the magnetic field vector.

Right-Hand Rule (for force)

To determine the direction of the magnetic force on a positive charge:

  • Point your thumb in the direction of the velocity ($v$).
  • Point your fingers in the direction of the magnetic field ($B$).
  • Your palm will push in the direction of the force ($F$).

Simulation: Charged Particle Motion

A positive charge entering a uniform magnetic field will experience a force causing it to move in a circular path. Click to reset.

Practice Problem 2

A proton (a positively charged particle) is moving from left to right. It enters a uniform magnetic field that is directed out of the page. What is the initial direction of the magnetic force on the proton?

Hint: Apply the Right-Hand Rule.

Solution to Problem 2

Using the Right-Hand Rule:

  • Your thumb points right (direction of velocity).
  • Your fingers point out of the page (direction of the magnetic field).
  • Your palm pushes upwards.

The initial magnetic force on the proton is upwards, perpendicular to both its velocity and the magnetic field.

Magnetic Induction

A changing magnetic field through a coil of wire induces an electric current. This is the principle behind Faraday's Law of Induction and the operation of electric generators.

Simulation: Induction Experiment

Move the magnet in and out of the coil to see the induced current light up the bulb.

Maxwell's Equations

These four equations are the foundation of classical electromagnetism, uniting electricity, magnetism, and optics. They describe how electric and magnetic fields are generated by charges, currents, and by each other.

Gauss's Law & Magnetic Gauss's Law

1. Gauss's Law for Electricity:

$$\nabla \cdot \mathbf{E} = \frac{\rho}{\varepsilon_0}$$

This equation states that electric fields originate from electric charges. The divergence of the electric field ($\nabla \cdot \mathbf{E}$) is proportional to the electric charge density ($\rho$).

2. Gauss's Law for Magnetism:

$$\nabla \cdot \mathbf{B} = 0$$

This states that there are no magnetic monopoles. The magnetic field lines always form closed loops, and the net magnetic flux through any closed surface is zero.

Faraday's & Ampere's Laws

3. Faraday's Law of Induction:

$$\nabla \times \mathbf{E} = - \frac{\partial \mathbf{B}}{\partial t}$$

A changing magnetic field ($\frac{\partial \mathbf{B}}{\partial t}$) creates a circulating electric field ($\nabla \times \mathbf{E}$). This is the principle of induced current.

4. Ampere-Maxwell's Law:

$$\nabla \times \mathbf{B} = \mu_0 \left( \mathbf{J} + \varepsilon_0 \frac{\partial \mathbf{E}}{\partial t} \right)$$

A magnetic field ($\nabla \times \mathbf{B}$) can be generated by an electric current density ($\mathbf{J}$) or by a changing electric field ($\frac{\partial \mathbf{E}}{\partial t}$). The latter term was Maxwell's crucial addition.