Know that a conductor moving across a magnetic field or a changing magnetic field linking with a conductor can induce an e.m.f. in the conductor

4.5.1 Electromagnetic Induction

Objective

Understand that a conductor moving across a magnetic field or a changing magnetic field linking with a conductor can induce an electromotive force (e.m.f.) in the conductor.

What is Electromagnetic Induction?

When a conductor (like a wire) moves through a magnetic field, or when the magnetic field around a conductor changes, an electric current is produced. This is called electromagnetic induction.

Why Does It Happen?

Think of a magnet as a “magnetic wind.” When a conductor cuts through this wind, it feels a force that pushes the electrons in the wire, creating a flow of charge – an e.m.f. The faster the conductor moves or the faster the field changes, the stronger the e.m.f.

Key Formula

The induced e.m.f. is given by Faraday’s law:

\$\mathcal{E} = -N \frac{d\Phi}{dt}\$

Where:

  • \$\mathcal{E}\$ – induced e.m.f. (volts)
  • \$N\$ – number of turns in the coil
  • \$\Phi\$ – magnetic flux (Wb)
  • \$\frac{d\Phi}{dt}\$ – rate of change of flux (Wb s⁻¹)

Magnetic Flux

Magnetic flux is the amount of magnetic field passing through a given area:

\$\Phi = B \, A \, \cos\theta\$

Where:

  • \$B\$ – magnetic field strength (T)
  • \$A\$ – area of the loop (m²)
  • \$\theta\$ – angle between the field and the normal to the area

Analogy: The “Magnetic Roller Coaster”

Imagine a roller coaster (the conductor) moving through a tunnel filled with invisible magnetic “winds.” As the coaster speeds up or slows down, the wind pushes against the cars, causing them to move. The faster the change, the stronger the push – just like a faster change in magnetic flux creates a stronger e.m.f.

Common Situations

  1. Moving a straight wire through a uniform magnetic field.
  2. Rotating a coil in a steady magnetic field (electric generators).
  3. Changing the strength of a magnetic field around a fixed coil (induction coils).

Sign Conventions (Lenz’s Law)

The negative sign in Faraday’s law tells us that the induced e.m.f. always opposes the change that produced it. This is known as Lenz’s law.

ScenarioDirection of Induced Current
Coil in a growing magnetic field (field increasing into the page)Counter‑clockwise (to create a field out of the page)
Coil in a decreasing magnetic field (field decreasing into the page)Clockwise (to maintain the field into the page)

Exam Tips

  • Always state the sign of the induced e.m.f. using Lenz’s law.
  • Check the direction of motion or field change before applying the formula.
  • Remember that the induced e.m.f. is proportional to the rate of change of flux – faster changes give larger e.m.f.
  • When a coil is rotated, use the right‑hand rule to determine the direction of the induced current.
  • For multiple-choice questions, look for statements that violate Lenz’s law – those are usually wrong.