Magnetic Fields and Forces: Understanding Electromagnetism

**Fe, Co, Ni: Ferromagnetic Materials**

_Iron (Fe), Cobalt (Co), and Nickel (Ni)_ are ferromagnetic materials. They strongly attract metals and exert attractive or repulsive forces on other materials.

**Early Discoveries in Magnetism**

• **William Gilbert:** Identified North and South Poles as magnetic.
• **First Discovered Natural Magnet:** Magnetite (iron oxide (Fe₃O₄)) and Magnesia (Chinese).

**Electric and Magnetic Fields**

• **Charge (Q) at rest:** Creates an electric field.
• **Moving charge:** Creates an electromagnetic field.

Analogy:

• Computer storage ↔ Electric field
• Mass ↔ Gravitational field
• Magnet ↔ Magnetic field

**Key Figures in Electromagnetism**

• **1831 Michael Faraday:**

  Introduced the concept of lines of force to explain the behavior of forces acting at a distance.

• **Pierre de Maricourt:**

  Realized that magnetic monopoles do not exist.

**Magnetic Field Properties**

1. Any magnetic field **line** runs from the north to the south magnetic pole.
2. **The intensity** of the magnetic field is directly proportional to the number of field lines per unit area.
3. **The magnetic field vector** (**B**) is tangential to the field line that passes through a given point.
4. Field **lines** never intersect.
5. Field **lines** are closed and continuous, even within the surface of a magnet.

• **Hans Christian Oersted:**

  Discovered that an electric current can produce magnetic fields, deflecting a nearby compass needle. This phenomenon is known as the Oersted effect.

• **André-Marie Ampère:**

  Discovered that two conductors carrying electrical currents can attract or repel each other like two magnets. Ampère proposed that natural magnetism arises from electric currents acting at the molecular level.

• **Michael Faraday:**

  Concluded that electric currents can be generated from varying electric fields.

• **1860: James Clerk Maxwell:**

  Concluded that magnetic fields can be created from varying electric fields.

• **Lorentz Force:**

  When an electrically charged particle enters a region with a homogeneous magnetic field (where all points have the same magnetic field), it experiences a diverting force known as the Lorentz force.

**J.J. Thomson Experiment**

In 1897, J.J. Thomson, using a cathode ray tube, experimentally determined the ratio between the electron's mass and charge, known as the electron's specific charge.

q/m: Specific charge of e^-

When an electron beam is subjected to a uniform magnetic field, it experiences a deviation due to the magnetic forces acting on it. Because of this deviation, the magnetic force acting on the beam equals the centripetal force acting on the electron beam. Therefore, we can establish the following equality:

q/m = 2V / (B² * R²)

q/m = 1.76 x 10¹¹ [C/kg]

**Magnetic Force on a Current-Carrying Conductor**

For a straight conductor of length L carrying a current I, arranged perpendicularly to a magnetic field of intensity B, the conductor experiences a magnetic force with a magnitude given by:

F = I * L * B

**Magnetic Force Between Two Parallel Conductors**

When two wires carrying electric currents are close together, they experience an attractive or repulsive force due to the interaction between the magnetic fields generated by the currents. The magnitude of the magnetic field at a distance r from a long, straight conductor of length L carrying a current I₁ is given by:

B₁ = μ * I₁ / (2πr)

If a second conductor of the same length L, carrying a current I₂, is placed at a distance r and parallel to the first conductor, it will experience a force whose magnitude is:

F = I₂ * L * B₁

F = μ * I₁ * I₂ * L / (2πr)