Induced EMF and magnetic flux

Physics > Induced EMF and magnetic flux

Consider electromotive force, magnetic flux and Faraday’s law of electromagnetic induction: change in magnetic flux in a magnetic field, galvanometer.

Faraday’s Law of Induction: An electromotive force is induced through a change in magnetic flux.

Learning challenge

  • Understand the relationship between magnetic field and electromotive force.

Key points

  • A change in the magnetic field flux causes an EMF.
  • The magnetic flux through the surface acts as a component of the magnetic field.
  • General formula of magnetic flux: ΦB = ∬AB ⋅ dA. This is the integral of the entire magnetic field passing through small sections dA.


  • Galvanometer is an analog current measuring device (G), which is based on the deflection of the needle created by the force of the magnetic field.
  • Vector area – a vector whose value is located in a specific area, and the direction is perpendicular to the surface area.

Induced EMF

The galvanometer was used by Faraday to demonstrate the ability of magnetic fields to create currents. When the switch is closed, the magnetic field is collected in a coil at the top of the iron ring and transported to the bottom ring. A galvanometer is used to detect the current induced in a separate coil at the bottom.

The Faraday apparatus shows the ability of a magnetic field to create a current. Changes due to the upper coil induce an EMF as well as a current in the lower coil. When the switch is opened / closed, the galvanometer registers the opposite direction of the currents. If the contact is off or open, then the current does not pass through the device

In the experiments, the scientist noticed that with the switch closed, the galvanometer finds a current moving in one direction at the bottom of the coil. But when open, the current changes direction. If you leave the switch in one position for a long time (open or closed), then the current stops moving. A change in the magnetic field generates a current.

The main electromotive force (EMF) also remains, which leads to it. The current is the result of the EMF created by the alternating magnetic field. Moreover, it is not affected by the presence of the current path.

Magnetic flux

Magnetic flux is a component of the magnetic field. It is proportional to the number of field lines penetrating the surface. Calculated by the formula:

ΦB = B ⋅ A = BAcosθ (B is the magnitude of the magnetic field, A is the surface area, and θ is the angle between the magnetic field lines and the perpendicular).

Let’s take a look at the magnetic flux for the infinitesimal element of the section dA, where we will consider the field constant:

All points on the surface have the same direction – the surface normal. The magnetic flux through the point acts as a component of the magnetic field along the normal direction

B = B ⋅ dA

Now the common surface A can be divided into infinitesimal elements, and the total magnetic flux will act as an integral of the surface:

ΦB = ∬A B ⋅ dA.

Physics Section

Magnetic flux, induction and Faraday’s law
  • Induced EMF and magnetic flux
  • Faraday’s law of induction and Lenz’s law
  • EMF movement
  • Back-EMF, Eddy Currents and Magnetic Damping
  • Changing the magnetic flux leads to an electric field
  • Electric generators
  • Electric motor
  • Inductance
  • Quantitative interpretation of the driving emf
  • Mechanical work and electrical energy
  • Energy in a magnetic field
  • Transformers
AC circuits
  • Self-induction
  • RL circuits
  • Serial RLC: high and low frequencies; Phasor circuit
  • AC Resistors
  • AC capacitors: capacitance and phase diagrams
  • AC inductors: inductive reactance and phase diagrams
  • Resonance in RLC circuits
  • Power
Application of induction and electromagnetic waves
  • Sound systems, computer memory, seismograph, VKZZ
  • Antenna
Magnetic fields and Maxwell’s forecast
  • Stored energy in a magnetic field
  • Maxwell’s predictions and Hertz’s confirmation

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