Magnetic Flux:
Magnetic flux is the product of the magnetic field strength and the area it penetrates, adjusted by the angle of incidence. It is a measure of the total magnetic field that passes through a given area. The magnetic flux is like the flow of the magnetic field through a surface. If you think of the magnetic field lines as arrows, the flux is the number of arrows passing through the surface, taking into account their angle. Think of it as the amount of magnetic field lines passing through a surface like a loop of wire. It is the key quantity that, when changed, induces an electric current in a circuit. Mnagnetic flux is measured in webers (Wb).
Imagine a loop of wire in a magnetic field. If you rotate the loop, the angle changes, so the flux changes. If you move the loop into or out of the field, the flux changes. If you change the strength of the magnetic field, the flux changes. Any change in flux induces a voltage.
Mathematical Expression:
For a constant magnetic field (B) passing through a flat surface (area A), the magnetic flux is given by,Φ = B × A × cos(θ)
where,
Φ = Magnetic flux (Webers, Wb)
B = magnitude of the magnetic
field (T)
A = area of the surface (m²)
θ = angle between the magnetic field lines and line perpendicular to the area.
We use cosine because the flux is maximized when the magnetic field is perpendicular to the surface, all field lines pass straight through. cos(0°) = 1. And zero when the magnetic field is parallel to the surface, no field lines pass through. cos(90°) = 0. At other angles, only the perpendicular component counts.
For non uniform magnetic fields or non flat surfaces, we break the surface into small pieces and sum up the flux through each piece.
φ = ∫ B dA
where dA is a vector of magnitude dA and direction normal to the surface,
and the dot product with B takes the Component of B perpendicular to the
surface.
Magnetic flux is crucial because a change in magnetic flux through a loop of wire induces an electromotive force (EMF) in the wire. This is Faraday's Law of Induction:
EMF = - dφ/dt
The negative sign indicates the direction of the induced EMF.
e.g.
• In generators, a coil rotates in a magnetic field which induces changing flux causing electricity.
• In ransformers, changing current in one coil creates changing flux, which induces voltage in nearby coil.
Explain how changing magnetic flux induces voltage?
Michael Faraday discovered in 1831 that if you change the magnetic field through
a coil of wire, you induce a voltage, and therefore a current if the circuit is closed. According to faraday's law of electromagnetic induction, a changing magnetic flux through a loop induces an electromotive force (EMF) or voltage in the loop. This is the principle behind generators, transformers, and many electrical devices.
How Does Changing Flux Induce Voltage?
Remember that magnetic flux, Φ = B × A × cos(θ) (for a uniform field and flat area).So, flux can change by:
• Changing the magnetic field strength B
• Changing the area A of the loop
• Changing the angle θ between the field and the normal to the area
When the flux through the loop changes (by any of the above means), it induces an electric field in the loop. This electric field is what pushes the charges and creates a voltage. A changing magnetic field produces an electric field. This is a fundamental fact, a time varying magnetic field creates a circulating (non-conservative) electric field. The induced electric field exists in space, whether there is a wire or not. If there is a wire loop, the electric field exerts a force on the free electrons, causing them to move.
e.g.
Moving a magnet into a coil
A bar magnet and a coil of wire connected to an ammeter. Push the north pole of the magnet into the coil. As the magnet approaches, the magnetic field through the coil increases. The changing flux induces a voltage in the coil. The voltage causes
a current to flow. The direction of the current is such that it creates a magnetic field that opposes the increase. So, the coil will create a north pole facing the approaching magnet to repel it.
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