PHY C23: Electromagnetic Induction

Before this, we have seen how a current-carrying conductor in a constant magnetic field will experience a force. Now we turn to the opposite of this effect:

  • EM Induction
    • Magnetic Flux Linkage
    • Factors affecting the magnitude of induced e.m.f.
    • Faraday’s Law

What is electromagnetic induction?
The effect where a changing magnetic flux can induce an e.m.f. in a circuit.

This means that if I have a conductor in a magnetic field, & the magnetic flux within that conductor CHANGES somehow, an e.m.f. will be produced which could drive current in the conductor.

A few things to note:

  • an e.m.f. will always be induced when there is a change of magnetic flux
    • we use the term ‘e.m.f.’ instead of ‘voltage’ because cutting the magnetic field PROVIDES electric potential energy to charges to move
  • a current is only induced when the circuit is complete (an incomplete circuit will cause an e.m.f. with no current in the conductor)

How does magnetic flux change?
There are a couple of ways to do so:

Area perpendicular to the field changes
 For example:

Source: Carl Adler
Strength of magnetic field changes
AKA Magnetic flux density (B) changes

 For example:
Ponor, CC BY-SA 4.0, via Wikimedia Commons
Conductor moves relative to the field lines

For example: 

Source: Yves Pelletier
Yes, I made those GIFs on the left myself

In these situations, we say that a conductor CUTS the magnetic field lines.
*REMEMBER: there will be no e.m.f. if conductor moves parallel to the field lines.

THIS is cutting:
This is NOT cutting:

In practice, it is inefficient to generate e.m.f. with a single wire cutting a magnetic field because the cross-sectional area A is very small.
Instead, multiple turns of wire are used to maximise A:

This is why we use coils in most induction devices.

Before we can explore the characteristics of EM Induction further, it’s time to introduce a new term:

Magnetic flux linkage

What is magnetic flux linkage?
The product of change of magnetic flux (ΔΦ) & the number of turns (N) of a conductor involved in the change of flux.

Magnetic flux linkage = NΔΦ

Basically, this gives the total change of magnetic flux of a circuit.

What are the factors affecting the MAGNITUDE of induced e.m.f.?
Experimentally, scientists have found that:

  • increasing cross-sectional area (A) of a single wire perpendicular to the field lines = larger e.m.f
  • increasing the number of turns in a coil (N) = larger e.m.f.
  • increasing strength of a magnet AKA magnetic flux density (B) = larger e.m.f.
  • decreasing time taken (t) in changing magnetic flux = larger e.m.f.

We can put these all together & explore QUANTITATIVELY how much e.m.f. is generated.

Faraday’s Law of EM Induction

The magnitude of e.m.f. induced is proportional to the rate of change of magnetic flux linkage.

Since Φ = BA, we can also express this as:

This fits in with our experiments: the faster we change the magnetic flux, the more e.m.f. induced!

Faraday’s Law tells us about the MAGNITUDE of e.m.f. induced, but how about the DIRECTION?

To understand that, we must dig a little deeper & ask “WHY is e.m.f. induced anyway?”

Let’s do just that… in the next post. See you there!

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