Glossary
Area Vector (A)
A vector whose magnitude is equal to the area of a surface and whose direction is perpendicular (normal) to the plane of the surface. For closed surfaces, it points outward.
Example:
For a flat circular coil, the area vector points straight out from the center of the coil, perpendicular to its plane.
Constant Magnetic Field Flux Formula (Φ_B = B ⋅ A)
This formula calculates magnetic flux when the magnetic field is uniform and constant across a flat surface, using the dot product of the magnetic field vector and the area vector.
Example:
To find the flux through a flat loop in a uniform magnetic field, you'd use Φ_B = B ⋅ A, where the angle between the field and the loop's normal is crucial for the dot product.
Dot Product (in context of flux)
A mathematical operation between two vectors that results in a scalar quantity, representing the product of their magnitudes and the cosine of the angle between them. In flux, it accounts for the orientation of the magnetic field relative to the area.
Example:
The dot product in Φ_B = B ⋅ A ensures that only the component of the magnetic field perpendicular to the surface contributes to the flux.
Electromagnetic Induction
The process by which a changing magnetic field through a conductor induces an electromotive force (EMF) and, consequently, an electric current.
Example:
Generators use electromagnetic induction to produce electricity by rotating coils of wire within a magnetic field.
Faraday's Law
States that the magnitude of the induced electromotive force (EMF) in a circuit is directly proportional to the rate of change of magnetic flux through the circuit.
Example:
A changing magnetic field from a moving magnet near a coil of wire will induce a current in the coil, as described by Faraday's Law.
Infinitesimal Area Element (dA)
A tiny, differential piece of a surface, represented by a vector whose magnitude is the differential area and whose direction is normal to that tiny piece of the surface.
Example:
When integrating to find total flux, we consider the magnetic field passing through each tiny infinitesimal area element to sum up the total.
Lenz's Law
States that the direction of an induced current or EMF is always such that it opposes the change in magnetic flux that produced it.
Example:
If you try to push a magnet into a coil, the induced current will create a magnetic field that repels the incoming magnet, illustrating Lenz's Law.
Magnetic Flux (Φ_B)
A measure of the total number of magnetic field lines passing through a given area. It quantifies how much magnetic field 'stuff' goes through a surface.
Example:
When a compass needle deflects near a current-carrying wire, it's responding to the magnetic flux created by the wire's magnetic field.
Scalar Quantity (Magnetic Flux)
A physical quantity that has magnitude but no direction. Magnetic flux is a scalar, where its sign indicates whether the field is entering or leaving a surface.
Example:
Magnetic flux is a scalar quantity, meaning it has a value like 5 Weber, but it doesn't point in a specific direction in space.
Total Magnetic Flux Calculation Formula (Φ_B = ∫ B ⋅ dA)
This integral formula is used to calculate the total magnetic flux through a surface when the magnetic field is non-uniform or varies across the area.
Example:
When calculating the flux through a large, irregularly shaped surface in a complex magnetic field, one must use the integral Φ_B = ∫ B ⋅ dA to sum up contributions from each infinitesimal area element.
Weber (Wb)
The SI unit of magnetic flux, defined as one tesla-meter squared (1 Wb = 1 T·m²).
Example:
A strong electromagnet might produce a magnetic flux of several Webers through a nearby loop.