Study Notes on Magnetism and Electromagnetic Induction

Magnetism: A physical phenomenon in which certain materials exert attractive or repulsive forces on other materials.
Materials that exhibit magnetism usually contain iron, nickel, or cobalt.
Types of Magnets:
- Natural Magnets: Found in nature (such as lodestone), possessing weak and irregular magnetic properties.
- Artificial Permanent Magnets: Man-made magnets created by magnetizing steel or other ferromagnetic materials that retain magnetism for an extended period. Commonly used in compasses, motors, and electronic devices.
- Electromagnets: Temporary magnets that are created when an electric current flows through a coil of wire wound around a soft iron core. Their magnetic strength can be influenced by adjusting the current, the number of turns in the coil, or the core material.

Ferromagnetic Materials (e.g., iron, cobalt, nickel):
- Strongly attracted to magnets,
- Can easily be magnetized,
- Most important for making permanent magnets and electromagnets.
Paramagnetic Materials (e.g., aluminum, platinum):
- Weakly attracted to a magnetic field,
- Lose their magnetism when the external field is removed.
Diamagnetic Materials (e.g., copper, bismuth, graphite):
- Weakly repelled by a magnetic field,
- Cannot be magnetized.

Magnetic Field: The region around a magnet or a current-carrying conductor in which magnetic forces can be detected.
Represents the area where magnetic materials or moving charges experience a force due to the presence of the magnet.
The strength and direction of a magnetic field can vary depending on the source.
Magnetic Field Lines: A visual concept that represents the strength and direction of the field at different points in space.
- Field lines emerge from the north pole and enter the south pole, forming closed continuous loops inside the magnet.

Denoted as ext{ϕ}, it is a measure of the total magnetic field passing through a given surface.
The unit is Weber (Wb).
Formula: ext{ϕ} = B imes A imes ext{cos} heta
- where:
- B = magnetic flux density [T]
- A = area
- heta = angle between the field and the surface normal.

Used to determine the direction of the magnetic field created by a current-carrying conductor:
1. Imagine holding the conductor in your right hand.
2. Point your thumb in the direction of the electric current.
3. The curl of your fingers shows the direction of the magnetic field lines encircling the conductor.

When current flows through a long straight wire, the magnetic field forms concentric circles around the wire.
The strength of the field depends on the current and decreases with distance from the wire.
Ampere's Law: Describes the relationship between magnetic field and electric current. The magnetic field B is proportional to the current I and inversely proportional to the distance r.
- Formula:
  H = rac{I}{2 ext{π}r}
- where:
- H = Magnetic field intensity.

Magnetic Circuit Model: Often used in the design of electric machines and transformers.
The magnetomotive force (mmf), measured in ampere-turns, replaces voltage in an electric circuit:
- ext{mmf} = ext{ℱ} = NI
- Where:
- N = number of turns,
- i = current.

The polarity of the mmf corresponds to the direction of flux:
- The positive end of the mmf source is where the flux exits.
- The negative end is where the flux reenters.

ℱ = rac{ϕ}{ℛ}
- Where:
- ext{ℱ} = magnetomotive force of the circuit [ampere-turns],
- ϕ = total flux of the circuit [Wb],
- ℛ = reluctance of the circuit [ampere-turns per weber].
Reluctance: Analogous to electrical resistance in electric circuits.

The magnetic circuit calculations are approximations. Typically accurate within about 5% due to factors like leakage flux and variations in permeability.

Magnetic Permeability: Assumed constant regardless of the applied mmf, though it changes with the state of magnetization in practice.
Saturation Curve: Represents the relationship of flux to mmf:
- Initial increases in mmf cause significant increases in flux (unsaturated region).
- Eventually, further increases in mmf result in smaller increases in flux as saturation is approached.

DC Magnetization Curve: Shows the relationship between magnetizing intensity H (A-turns/m) and uncertainty of induced flux density B (T).
Operating in the unsaturated range yields maximum efficiency.

Electromagnetic Induction: Electric current can be induced in a conductor when there is relative motion between the conductor and a magnetic field.
Two Fundamental Laws:
- First Law: An electromotive force (EMF) is induced in a conductor whenever the magnetic flux linked with it changes.
- Second Law: The magnitude of the induced EMF is directly proportional to the rate of change of magnetic flux linkage.
Mathematical Expression: ext{e}_{ ext{ind}} = N rac{dϕ}{dt}
- where:
- ext{e}_{ ext{ind}} = voltage induced in the coil [V],
- N = number of turns of wire,
- dϕ = change of magnetic flux passing through the coil, and
- dt = time interval during which the flux change occurs.

Magnetic fields induce forces on a current-carrying wire within the field.
The induced force on a conductor is given by: F = i (l imes B)
- Where:
- i = magnitude of current [A],
- l = active length of the conductor [m],
- B = magnetic flux density [T].
Direction of Force: Determined by the right-hand rule:
- Index finger points in the direction of the current i, middle finger points in direction of flux density B, thumb gives the direction of force.

When a wire moves through a magnetic field, a voltage is induced: e_{ ext{ind}} = v imes B imes l
- Where:
- v = velocity of wire [m/s],
- B = magnetic flux density [T],
- l = active length of the conductor [m].