A variable magnetic field induces an electric field and vice versa.

Electromagnetic Induction

The electromagnetic induction is the electrical current generated in a closed circuit when there is relative motion between the circuit and an external magnetic field. The generated current is called induced current. This induced current will appear whenever variation of the magnetic flux happen through the area enclosed by the circuit, that is, whenever the intensity of the magnetic field changes, or by changing the area of the circuit with time, or changing the angle between the circuit and the magnetic field with the time.

Definitions

Magnetic Induction Flow \((\Phi)\)
In a closed circuit, the magnetic induction flow is equal to the number of induction lines that pass through the surface. The flow module of the magnetic induction through a closed surface is zero. The magnetic flux through a flat surface area \(A\) in a uniform magnetic field \(B\), making an angle \(\alpha\) with the plane normal vector is given by: $$ \Phi = A \cdot B \cdot cos( \alpha ) $$ the unit of magnetic flux in the \(IS\) is the Weber $$[\Phi] = Wb = \frac{kg.m^2}{s^{2}.A} = Tm^2 = Vs = \frac{J}{A}$$
Inductor
An inductor is a device that can be used to create a magnetic field within a known region. In practice the typical example of an inductor is the solenoid, a wire shaped as if it were a spring. We can also define the inductor as a device that stores magnetic energy, when it is traversed by an electric current. An inductor is characterized by its inductance \(L\). If the current \(i\) crosses the \(N\) turns of an inductor, the magnetic flux transverses the coil. The inductance is given by: $$ L = \frac{N \Phi}{i},$$ and its unit is the Henry, \([L]=H\).
Self-inductance
It is generated by the flow of the magnetic field produced by its own electric current of the circuit. The characteristics of self-inductance for a circuit are:
  • The induced current is against the variations in the circuit current.
  • When the current in the circuit increases, the self-inductance tends to decrease it, and when the current decreases, the self-inductance tends to increase it.
The self-inductance unit in \(SI\) is the Henry \((H)\): $$ H = \frac{Wb}{A} = \frac{Vs}{A} = \frac{kg.m^2}{s^{2}.A^2} $$
Self-induced EMF
Whenever there is a variation in the intensity of the current, for a circuit in a magnetic field, there will be a variation of the field flux through the area enclosed by the circuit. Consequently, the circuit will have an electromotive force self-induced. Mathematically, we have $$ \mathscr{E} = - L \left( \frac{\Delta i}{\Delta t} \right),$$ where \(L\) is the inductance, a constant that depends on the circuit's geometry.

Faraday's Law

Every time the magnetic flux through the area enclosed by a closed circuit varies over time, this circuit will have an induced electromotive force, given by:$$ \mathscr{E} = - \frac{\Delta \Phi}{\Delta t}.$$

Lenz's Law

It is about the tendency of systems to resist changes. It is also a practical rule for determining the direction of induced current in a circuit.

The direction of an induced current is such that it opposes any change in the electric current. And the induced magnetic field, generated by this induced current, will also have a direction to try to avoid changes in the magnetic flux.

Transformer

These devices can change the potential difference of a circuit, increasing it or decreasing it. However, they only work in circuits of alternated currents.

A simple model for a transformer consists of two very close and parallel coils, but without electrical contact. When an alternating current is applied to one coil (primary coil), this generates a variable magnetic field that induces a current in the other coil (secondary coil) according to Faraday's law.

If the number of turns in the primary coil \((n_p)\) is greater than the turns in the secondary coil, \((n_s < n_p) \) , the transformer will lower the output voltage in the secondary coil, and vice versa. The formula which relates the voltages \((\mathbb{V})\), current \((i)\) and the number of turns \((n)\) is: $$ \frac{\mathbb{V}_s}{\mathbb{V}_p} = \frac{n_s}{n_p} = \frac{i_s}{i_p}. $$ However, this formula is extremely simplified because there are many factors that modify the output voltage of the transformer, such as heating, the material used, geometry, construction , etc.

Relativity of Electric and Magnetic Phenomena

When a conducting bar has a translational movement in the region of a magnetic field, the force acting on the free electrons of the bar can be considered electrical or magnetic, depending on the adopted referential.