Glossary
Amperian Loop
An imaginary closed path chosen strategically to apply Ampère's Law, simplifying the calculation of magnetic fields due to current distributions. The choice of loop is crucial for simplifying the integral.
Example:
To find the magnetic field inside a long solenoid, one would choose a rectangular Amperian Loop that partially extends inside and outside the solenoid, leveraging the field's uniformity.
Ampère's Law
A fundamental law in electromagnetism that relates the line integral of the magnetic field around a closed loop to the total current passing through the loop. It is used to calculate magnetic fields produced by steady currents, especially in situations with high symmetry.
Example:
Using Ampère's Law, a student can efficiently calculate the magnetic field strength at a certain distance from a long, straight current-carrying wire without complex integration.
Biot-Savart Law
A law that calculates the magnetic field produced by a steady current, providing a way to determine the magnetic field at any point in space due to an infinitesimal current element. It is more general than Ampère's Law but often more complex to apply.
Example:
While Ampère's Law is ideal for highly symmetric current distributions, the Biot-Savart Law would be necessary to calculate the magnetic field at the center of a square current loop, where symmetry is less helpful.
Faraday's Law
States that a changing magnetic flux through a loop of wire induces an electromotive force (EMF) in the loop, which in turn can drive an induced current. This principle is fundamental to generators and transformers.
Example:
When a magnet is moved quickly through a coil of wire, a current is generated in the coil, demonstrating Faraday's Law of electromagnetic induction, which is how electric generators work.
Magnetic Field Inside a Long Solenoid
A uniform magnetic field created within a long coil of wire (solenoid) carrying a current. Its strength depends on the current and the number of turns per unit length, and it is largely confined to the interior of the solenoid.
Example:
An electromagnet can be created by winding wire into a solenoid; the strong, uniform Magnetic Field Inside a Long Solenoid can then be used to pick up metal objects or actuate switches.
Magnetic Field around a Long, Straight Wire
The magnetic field produced by a long, straight current-carrying wire, which forms concentric circles around the wire. Its strength is inversely proportional to the distance from the wire and directly proportional to the current.
Example:
A compass placed near a power line would align itself with the circular Magnetic Field around a Long, Straight Wire, indicating the direction of the field lines.
Maxwell's Addition (to Ampère's Law)
An extension to Ampère's Law proposed by Maxwell, stating that a changing electric field (often called displacement current) also produces a magnetic field. This addition completed the symmetry between electric and magnetic phenomena.
Example:
During the charging of a capacitor, even in the gap between the plates where no conduction current flows, a magnetic field is produced due to Maxwell's Addition to Ampère's Law, caused by the changing electric field.
Maxwell's Equations
A set of four fundamental equations that describe how electric and magnetic fields are generated by charges and currents, and how they interact with each other. They form the complete foundation of classical electromagnetism.
Example:
The existence of electromagnetic waves, like light and radio waves, is a direct consequence predicted by Maxwell's Equations, showing the interconnectedness of electric and magnetic phenomena.
Permeability of free space (μ₀)
A fundamental physical constant representing the ability of a vacuum to support the formation of a magnetic field. It is a key component in formulas for magnetic field strength in a vacuum.
Example:
When calculating the magnetic field inside a solenoid, the constant permeability of free space (μ₀) is used to determine the field's magnitude, reflecting how easily magnetic fields are established in a vacuum.
Superposition of Magnetic Fields
The principle stating that the total magnetic field at any point due to multiple current sources is the vector sum of the individual magnetic fields produced by each source. Direction and magnitude must both be considered.
Example:
To find the net magnetic field at a point between two parallel current-carrying wires, one must apply the Superposition of Magnetic Fields principle, adding the vector contributions from each wire.