Electromagnetism Principles: Biot-Savart, Ampere, and Faraday Laws

Biot-Savart Law

The Biot-Savart law describes circuits by assigning a character vector: the current element I dl. Here, μ₀ is the constant of proportionality known as permeability, where I is the current, dl is the element vector, u is the unit vector in the direction of the line connecting the element dl to point P, and r is the distance from the conductor element dl to point P.

Ampere's Theorem

The circulation of the magnetic field is the integral along a path of the vector dot product of magnetic induction B and the path element dl. The circulation of the magnetic field on a closed curve C is the product of permeability μ₀ and the intensity of electric current I_c that crosses the surface bounded by the closed curve C. This theorem is used to determine the magnetic induction of a solenoid.

Lenz's Law

The induction of an electric current in a circuit is due to the variation of magnetic flux through the circuit. The direction of the induced current is such that it opposes the cause that produces it.

Faraday's Law

The electromotive force induced in a circuit equals the rate of change of the magnetic flux through the circuit, with an opposite sign.

Henry's Experiment

A magnetic field induces an electromotive force. If a conductor moves perpendicular to a magnetic field, a potential difference is created. The electromotive force induced is explained by the Lorentz force:

• A conductor of length l moves in a constant uniform magnetic field directed into the paper.
• The accumulation of negative charge at the lower end and positive charge at the upper end generates an electric field E along the conductor.
• The magnetic force F_m is compensated by the electric force F_e.
• The electromotive force is maintained only while the conductor moves within the magnetic field.

Generating Electricity

An electric generator is any device that transforms one form of energy into electrical energy:

• Dynamo: Produces continuous electrical current.
• Alternator: Produces alternating current.
• Electric engine
• Galvanometer
• Electric buzzer

Inductance

If the intensity of the current running through an electrical circuit varies, the magnetic field and the magnetic flux also vary. Consequently, an electromotive force is induced by the variation of the intensity of the circuit; this phenomenon is called inductance. The constant of proportionality is the inductance, which depends on the physical characteristics of the electric circuit, such as the material type and geometric shape.