How to Calculate Induction Currents, Voltage & Loops

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  • 0:04 What Is Magnetic Flux?
  • 2:56 Applications
  • 4:05 An Example
  • 6:18 Lesson Summary
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Lesson Transcript
Instructor: Matthew Bergstresser

Matthew has a Master of Arts degree in Physics Education. He has taught high school chemistry and physics for 14 years.

When closed loop conductor experiences a change in magnetic flux, a voltage is produced, which induces an electrical current. In this lesson, we will investigate how voltages and electrical currents are generated by changes in magnetic flux.

What Is Magnetic Flux?

Have you ever lost your balance and then recovered so you didn't fall down? This is an effective analogy for how electric conductor loops function when they experience a change in magnetic flux. Magnetic flux is the amount of magnetic field penetrating perpendicularly through an area.

A magnetic field is generated from the wire loop in a direction so as to keep the magnetic flux through the loop constant. It tries to balance out the changing magnetic flux. An induced voltage generates an induced electric current, which generates the new magnetic field.

We use a • to represent a magnetic field pointing out of the screen, and an × to represent a magnetic field into the screen. The diagram on your screen shows a loop of wire moving into a magnetic field. The arrows represent the direction the current flows in the loop.

Diagram 1. Wire loop moving to the right into the magnetic field.

In this diagram, the magnetic field inside the wire loop is increasing out of the screen because the coil is moving from a small amount of magnetic field into a greater amount of magnetic field. The conductor wants to decrease this increasing magnetic field. To do that it induces a current moving clockwise because that will generate a magnetic field pointing into the screen. The way you can tell which way the current will flow is to point your right thumb in the direction the magnetic field needs to increase to keep the net magnetic constant. Your right fingers curl in the direction of the induced current.

A voltage must exist to push a current. Faraday's law relates the change in magnetic flux and the number of loops of the conducting material to the voltage generated in the loop. The equation on your screen shows Faraday's law.

Equation 1

  • ΔV is the voltage generated in volts
  • N is the number of loops in the coil
  • ΔΦ is the change in magnetic flux due to a loop-area change and/or a magnetic flux change in Webers (Wb)
  • t is time required for ΔΦ change in seconds (s)

The equation for magnetic flux (Φ) is given in the following equation:

Equation 2

  • Φ is magnetic flux in Webers (Wb)
  • B is the magnetic field strength in Tesla (T) perpendicular to the coil.
  • A is the area of the loop in square meters (m2)

We can use Ohm's law, which is written as V = IR, to calculate amperage after the voltage has been determined. Let's look at some applications of Faraday's law.


Transformers are devices used to increase or decrease voltage. They consist of an iron metal core shaped like a picture frame. On either side of the iron core are loops of wire. The primary coil voltage affects the secondary coil voltage. If the secondary coil has more loops than the primary coil, the voltage is stepped up to a higher voltage. If the secondary coil has less loops than the primary coil, the voltage is stepped down to a lower voltage. This is used in electricity transmission from electric power plants to residences and businesses.

Electric toothbrushes get charged using the phenomenon of induced voltage. Inside the charging device is a coil of wire. The charging device has a coil that experiences a changing magnetic field due to the alternating current in the house's electrical system. Since the magnetic field is changing due to the alternating current, a current is induced in the coil, which charges the electric toothbrush.

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