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EEE Components, PASSIVES

Magnetic Induction (B) and Flux (F). Faraday’s Law explanation

  • Posted by Tomáš Zedníček
  • On March 5, 2019
  • 2

Magnetic induction B

A potential is induced in a conductor loop if the magnetic field passing through the conductor loop changes with time.

Featured Image Fig. 1.10: Experimental configuration for magnetic induction

The surge in potential over the area of the loop is known as the magnetic induction B. Like the magnetic field strength, the magnetic induction B is a vector quantity.

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The following relationship applies for the magnetic induction B:

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The magnetic induction (B) is the quotient of the induced potential surge:

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and the product of the winding turns (N) and the windings area (A) of the induction coil.

The unit of magnetic induction (B) is the Tesla (T) = Vs/m2.

The magnetic induction B and the field strength H are proportional to one another.

The constant of proportionality is the magnetic field constant (μ0), given by experimental measurement.

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In vacuum and also with sufficient accuracy for air, this leads to:

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The magnetic induction (BL) in air for the above example is given by:

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Magnetic flux F

The magnetic flux (F) is the scalar product of the magnetic flux density (B) and the area vector (dA).

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If (B) passes perpendicular through the area and the field is homogenous:

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The unit of magnetic flux (F) is the same as that of the voltage surge (Vs) (Voltsecond) or Weber (Wb).

Faraday’s law

Up until now we have considered static magnetic fields. If the magnetic flux changes with time, a voltage U is induced (Faraday’s law).

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U = induced voltage
t = time

The polarity of the voltage is such that a current is generated on closing a circuit whose induced magnetic field opposes the original magnetic flux, i.e. it tends to reduce the magnetic field (Lenz’s rule – Figure).

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Figure : Representation of Lenz’s rule. The imposed magnetic field induces a current in the direction such that its induced magnetic field opposes the imposed field

Taking a winding with N turns, Faraday’s law can be expressed in the following form.

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A = cross section of the coil
l = length of the coil or of the magnetic circuit
I = current through the coil
L = inductance of the coil [H(enry) = Vs/A]

So the inductance limits the change in current once a voltage is applied. It can be calculated from the coil data:

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AL = AL value; mostly in nH/N2

The energy stored in the magnetic field is subject to the following relationships:

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The energy stored in volume V is composed of both the magnetic field strength H and the magnet flux density B. For transformers and chokes with ferromagnetic cores, the flux density is limited by saturation (see chapter I/1.5) and is constant throughout the magnetic circuit. If an air gap is introduced (material with permeability μ~1), the field strength is highest in this air gap with H = B/μ. It follows that the energy density is highest in the air gap. One also speaks of the energy being stored in the air gap.

Comparing magnetic fields with electrical fields, analogies emerge between certain parameters. These are summarised in the Table below:

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Tab. :  Analogies between magnetic and electric fields
  • Author
  • Recent Posts
Tomáš Zedníček
Tomáš Zedníček
Founder & President of  the EUROPEAN PASSIVE COMPONENTS INSTITUTE (EPCI)
EPCI | Bringing Passive Professionals Together

Electrotechnology Degree by Technical University of Brno, the Czech Republic in 1993
Ph.D. in Tantalum Capacitors in 2000
> 21 years working for tantalum capacitor manufacturer
> 15 years in a position of Worldwide Technical Marketing Manager
more than 60 technical papers and 1 US/international patent
4 outstanding/best award technical papers at CARTS passive component conference
2005 Dr. Zandman award for a great contribution to the passive component industry
Lecturer of capacitor technologies, presentation skills, and inter-culture communication
July 2015 – Founder of the European Passive Components Institute
Tomáš Zedníček
Latest posts by Tomáš Zedníček (see all)
  • Why low ESR matters in capacitor design - May 24, 2021
  • Voltage and Frequency Dependence on Resistors - March 6, 2021
  • Permeability concept in Inductors - March 4, 2021
TAGS: INDUCTOR MAGNETIC FLUX Inductors

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2 comments on Magnetic Induction (B) and Flux (F). Faraday’s Law explanation
Pranakrushna sahoo
  • Sep 18 2021
Good explanation
    doEEEt Media
    • Sep 23 2021
    Thank you for your support
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