4.5.1 Electromagnetic Induction
What is Electromagnetic Induction?
When a conductor moves through a magnetic field, or the magnetic field around a conductor changes, an electric current is produced. This is the principle behind generators, transformers and many everyday devices.
Key Concept: Relative Directions
To predict the direction of the induced current, we must understand the relationship between three vectors:
- Force on a charge – given by the Lorentz force law: \$F = q(\mathbf{v} \times \mathbf{B})\$
- Magnetic field – direction of the magnetic lines of force.
- Induced current – direction of flow of positive charges (conventionally).
Use the right‑hand rule for the cross product and Lenz’s law to determine the induced current.
Right‑Hand Rule (Force on a Moving Charge)
Hold your right hand so that:
- Index finger points in the direction of the velocity \$\mathbf{v}\$ of the charge.
- Middle finger points in the direction of the magnetic field \$\mathbf{B}\$.
- Thumb then points in the direction of the force \$\mathbf{F}\$ on a positive charge.
⚡️ Example: If a wire moves to the right (\$\mathbf{v}\$) through a magnetic field pointing into the page (\$\mathbf{B}\$), the force on a positive charge points upward.
Lenz’s Law (Direction of Induced Current)
The induced current always flows so that its magnetic field opposes the change that produced it.
🔄 Example: A coil is pulled out of a magnetic field. The magnetic flux through the coil decreases. The induced current will flow in a direction that creates a magnetic field pointing into the page, trying to keep the flux the same.
Putting It All Together – A Step‑by‑Step Guide
- Identify the change: Is the conductor moving, or is the magnetic field changing?
- Determine the direction of motion or field change.
- Apply the right‑hand rule to find the direction of the force on positive charges.
- Use Lenz’s law to decide the direction of the induced current that opposes the change.
- Check your answer by ensuring the induced magnetic field opposes the change.
Exam Tip Box
📝 Remember:
- Always use the right‑hand rule for \$\mathbf{v} \times \mathbf{B}\$.
- When in doubt, draw a quick sketch of the wire, the magnetic field lines, and the direction of motion.
- For induced currents, think “opposite to the change” – that’s Lenz’s law.
- Check the sign of the charge: the rules are for positive charges; for electrons, reverse the direction.
Good luck, and keep practicing with quick sketches – they’re the fastest way to avoid mistakes!
Quick Reference Table
| Scenario | Velocity (\$\mathbf{v}\$) | Magnetic Field (\$\mathbf{B}\$) | Force on +q (\$\mathbf{F}\$) | Induced Current Direction |
|---|
| Wire moves right, \$B\$ into page | → | ⊗ | ↑ | Counter‑clockwise (opposite to flux decrease) |
| Coil pulled out of field | – | ⊗ | – | Clockwise (creates field into page) |