(455) HL Flux and Faraday's law [IB Physics HL]
Introduction to Flux and Faraday's Law
The concept of flux is related to magnetic fields.
Flux differs from the fictional "flux capacitor" from the movie "Back to the Future."
Definition of Flux
Flux (Φ): represents the quantity of magnetic field lines passing through a given area.
Equation: ( \Phi = B \cdot A \cdot \cos(\theta) )
( B ): Magnetic field strength (measured in Teslas)
( A ): Area of the surface (measured in square meters)
( \theta ): Angle between the magnetic field and the normal to the surface.
Key Concepts of Flux
The flux is concerned with how many magnetic field lines intersect the surface area.
The angle ( \theta ) must be measured from the normal to the surface, not from the surface itself.
Faraday's Law
Definition of Faraday's Law
Statement: The induced electromotive force (EMF) is proportional to the rate of change of magnetic flux linkage.
Equation: ( E = -N \frac{d\Phi}{dt} )
( E ): Induced EMF (measured in volts)
( N ): Number of turns in a coil
( \frac{d\Phi}{dt} ): Rate of change of magnetic flux linkage.
Explanation of Faraday's Law
Induced EMF occurs only when there is a change in the magnetic flux environment.
The negative sign indicates the induced EMF opposes the change (Lenz's Law).
Insights on Magnetic Flux Linkage
Movement of magnetic field lines induces a potential difference (voltage) across a conductor.
Example: If a magnet is moved near a conductor, changing magnetic flux induces an EMF.
Induced EMF from a Moving Wire
Equation: ( E = B \cdot V \cdot L )
( V ): Velocity of the wire (in meters per second)
( L ): Length of the wire (in meters)
Example Calculation
Given:
Magnetic field strength (B) = 10^(-5) Teslas
Speed (V) = 200 m/s
Length of wings (L) = 30 m
Calculate induced EMF:
( E = 10^{-5} \cdot 200 \cdot 30 )
Result: ( E = 0.06 ) volts.
Conclusion
Understanding flux and Faraday's law is fundamental in electromagnetism.
The concepts help explain how electricity can be generated through the movement of magnetic fields.