For IB Physics HL, the induced electromotive force (emf) in a straight conductor moving perpendicularly through a uniform magnetic field is calculated using . Multiply the magnetic field strength, conductor speed, and effective conductor length within the field.
A charge carrier moving with the conductor experiences a magnetic force:
This applies when the velocity is perpendicular to the magnetic field. The magnetic force moves positive and negative charges toward opposite ends of the conductor, producing charge separation and an electric field inside it.
At equilibrium, the magnetic and electric forces balance:
The potential difference across a conductor of length is . Therefore:
| Quantity | Meaning and unit |
|---|---|
| Induced emf in volts (V) | |
| Magnetic field strength in tesla (T) | |
| Speed perpendicular to the field in | |
| Length of conductor cutting the field in metres (m) |
For example, a conductor moves at perpendicular to a field:
If the velocity is at an angle to the field, use only the perpendicular component, , so , provided the rod is oriented appropriately. Motion parallel to the field gives zero emf because the magnetic force on each charge is zero.
Determine polarity using the right-hand rule for for a positive charge. The end toward which positive charge is driven becomes positive; electrons move oppositely. This agrees with Lenz's law.
A current flows only if the conductor forms part of a closed circuit. Its direction can be determined from the magnetic force direction on positive charge; electrons move oppositely.
A common misconception is that means the conductor's total length. It is the effective length inside the field and oriented along the charge separation.
This is syllabus topic D.4 Induction (HL only). For a Calculate question, show the equation, substitution, and final value. Check that , , and are mutually perpendicular before using directly.
