Electromagnetism: Induction, Materials, and Laws
Chapter 8: Electromagnetic Induction
Induced Current
The current induced in a coil conductor opposes the change that created it. If the magnetic flux has a negative derivative, the induced field will try to maintain the existing field by creating a field in the same direction. If the derivative is positive, the negative sign indicates that the induced field will oppose the change, preventing the field from growing.
Electromotive Force (EMF)
The first two terms of the EMF depend on the temporal variation of the magnetic field, regardless of how it’s produced. The second term relates to the geometric deformation or movement of the conductor in which the induction occurs.
Producing Induced Current
To produce induced current, we vary the magnetic flux. This can be achieved by:
- Moving a magnet closer to or further from a loop.
- Moving coils closer to or further from each other.
- Rotating coils relative to each other.
- Varying the current in one of two coils over time.
Generating an Induced Electric Field
To generate an induced electric field, there must be a time-varying magnetic field. This time-varying magnetic field produces an electric field that propagates independently of any material medium.
Self-Induction
Induction can be produced by the current flowing in a solenoid or coil, creating self-induced current. This current generates a time-varying magnetic field, resulting in induction within the loop itself, as it’s immersed in its own magnetic flux.
Mutual Inductance
Two turns next to each other carry currents I¹ and I². The magnetic flux passing through the coils depends on the magnetic field of each, according to the definition of inductance.
Eddy Currents
When the magnetic flux changes, it induces currents called eddy currents.
Transformers
Transformers are used to increase or decrease voltage. The laminated iron core concentrates the magnetic field, maximizing the flux through the windings. This increases efficiency and reduces power dissipation.
Chapter 9: Magnetic Materials
Paramagnetic Materials
In paramagnetic materials, the magnetic moments of atoms or molecules tend to align with an external magnetic field. The magnetic moments of unpaired electrons are randomly oriented in the absence of a field. These materials are weakly attracted by strong external fields. Their susceptibility is almost independent of temperature and, in most cases, small.
Diamagnetic Materials
In diamagnetic materials, an external field induces currents that oppose the external field. When atoms or molecules have a total spin of zero, the predominant behavior is diamagnetism. These materials are slightly repelled by external fields. They are always weakly repelled by very intense external fields, a characteristic of almost all materials in nature. Their susceptibility is negative.
Ferromagnetic Materials
Ferromagnetic materials are strongly attracted by external magnetic fields. The magnetic moments of unpaired electrons are all aligned. Residual magnetization, or remanence, is the magnetization that remains after the external field is removed. Materials with high remanent magnetization are called hard ferromagnets, while those with low remanent magnetization are called soft ferromagnets. Above the Curie temperature, the material becomes paramagnetic.
Antiferromagnetic Materials
In antiferromagnetic materials, the magnetic moments are aligned in opposite directions.
Ferrimagnetic Materials
In ferrimagnetic materials, the spins are aligned in opposite directions, but the number of spins in one direction is different from the other, resulting in a net magnetic moment.
Intrinsic Time
Besides very weak diamagnetic behavior, there is also very weak paramagnetic behavior.
Magnetic Domains
Magnetic domains are small regions within the microscopic structure formed by atoms whose magnetic moments have a preferred alignment, which cannot be easily changed by thermal vibrations.
Curie Temperature
The Curie temperature is the temperature at which the alignment of domains can be broken.
Origin of Magnetism
Atomic magnetism is due to both the orbital magnetic moment (L) and the spin angular momentum (S).
Hard Magnetic Materials
Hard magnetic materials are used as permanent magnets due to their large remanent magnetization and coercive field, resulting in a hysteresis loop with a large area.
Soft Magnetic Materials
Soft magnetic materials are easily magnetized and demagnetized with the removal of the external field. They are used in transformer cores and solenoid cores.
Chapter 10: Fundamental Laws of Electromagnetism
1. Gauss’s Law for Electric Fields
Gauss’s Law for Electric Fields states that the flux of the electric field through a closed surface (S), called a Gaussian surface, is proportional to the electric charge enclosed within the surface.
2. Gauss’s Law for Magnetic Fields
Gauss’s Law for Magnetic Fields states that the magnetic flux through a Gaussian surface is always zero. This means that magnetic field lines never diverge or converge to a point, as magnetic poles are inseparable, implying the non-existence of magnetic monopoles.
3. Ampere-Maxwell’s Law
Ampere-Maxwell’s Law states that the circulation of the magnetic field vector along any closed path is proportional to the sum of the total current enclosed by the path and the time rate of change of the electric flux through the surface bounded by the path.
4. Faraday-Lenz’s Law
Faraday-Lenz’s Law states that the electromotive force (EMF) induced around a closed path is proportional to the negative of the time rate of change of the magnetic flux through the surface bounded by the path.