Glossary
Cross-sectional area (A)
The cross-sectional area of a solenoid refers to the area of its core, directly affecting its inductance.
Example:
Using a wider core, which increases the cross-sectional area (A), can boost a solenoid's inductance.
Energy Stored in an Inductor (U_L)
Inductors store energy in the magnetic field generated by the current flowing through them, proportional to the inductance and the square of the current.
Example:
When a large current flows through a powerful electromagnet, a significant amount of energy stored in an inductor (U_L) is held within its magnetic field.
Faraday's Law
Faraday's Law states that a changing magnetic flux through a coil induces an electromotive force (EMF) in the coil.
Example:
The operation of an electrical generator relies on Faraday's Law to produce electricity by rotating coils within a magnetic field.
Induced EMF (ε_i)
An induced electromotive force (voltage) is generated across an inductor when the magnetic flux through it changes, opposing the change in current.
Example:
Rapidly turning off a circuit with a large inductor can create a high induced EMF (ε_i), potentially causing a spark.
Inductance (L)
Inductance is a measure of a conductor's opposition to changes in the current flowing through it, acting like electrical inertia.
Example:
A large inductance in a circuit will cause the current to build up slowly when a voltage is applied, preventing sudden surges.
Inductor
An inductor is a passive electrical component, typically a coil of wire (like a solenoid), designed to have significant inductance and store energy in its magnetic field.
Example:
In an old radio, an inductor might be used to tune into different frequencies by varying its inductance.
Law of Conservation of Energy
This fundamental principle states that energy cannot be created or destroyed, only transformed from one form to another.
Example:
When an inductor discharges, its stored magnetic energy is converted into heat in a resistor, demonstrating the law of conservation of energy.
Length of the solenoid (ℓ)
The length of the solenoid refers to the physical extent of the coiled wire, inversely affecting its inductance.
Example:
A shorter length of the solenoid (ℓ), while keeping other factors constant, will result in higher inductance.
Lenz's Law
Lenz's Law specifies that the direction of the induced current or EMF opposes the change in magnetic flux that produced it.
Example:
When you push a magnet into a coil, the induced current creates a magnetic field that pushes back against the magnet, illustrating Lenz's Law.
Magnetic permeability of the core (μ_core)
This property describes how easily a material can support the formation of a magnetic field within itself, significantly influencing a solenoid's inductance.
Example:
Replacing an air core with a ferromagnetic material, which has a much higher magnetic permeability of the core (μ_core), dramatically increases the solenoid's inductance.
Number of turns (N)
For a solenoid, the number of turns refers to how many times the wire is coiled, directly affecting its inductance.
Example:
To increase the inductance of a solenoid, a designer might increase the number of turns (N) in its coil.