Know that the direction of an induced e.m.f. (electromotive force) always opposes the change that produces it.
Key Concepts
Changing magnetic flux through a circuit induces an e.m.f. (Faraday’s law).
The induced e.m.f. creates a current whose magnetic effect opposes the original change (Lenz’s law).
Direction can be found using the right‑hand rule for generators.
Faraday’s Law
The magnitude of the induced e.m.f. (\$\mathcal{E}\$) is proportional to the rate of change of magnetic flux (\$\Phi\$):
\$\mathcal{E} = -\frac{\Delta \Phi}{\Delta t}\$
The negative sign expresses Lenz’s law – the induced e.m.f. opposes the change in flux.
Lenz’s Law – Qualitative Form
When a magnetic flux through a closed conducting loop changes, an induced current flows in such a direction that its own magnetic field opposes the change in the original flux.
Determining the Direction of the Induced e.m.f.
Identify the cause of the change (e.g., a magnet moving towards the coil).
Determine whether the magnetic flux through the coil is increasing or decreasing.
Apply the right‑hand rule for generators:
Point the thumb in the direction of the conductor’s motion relative to the magnetic field.
Point the fingers in the direction of the magnetic field lines (from north to south).
The palm then faces the direction of the induced e.m.f. (conventional current) in the conductor.
Check that the resulting induced magnetic field opposes the original change. If it does not, reverse the direction.
Examples
Example 1 – Magnet Approaching a Coil
A north pole of a bar magnet is moved towards a stationary coil.
Flux through the coil is increasing into the page.
To oppose this increase, the induced magnetic field must point out of the page.
Using the right‑hand rule, the induced current must be anticlockwise when viewed from the magnet side.
Example 2 – Rotating a Loop in a Uniform Magnetic Field
A rectangular loop rotates clockwise in a uniform magnetic field directed into the page.
When the plane of the loop is moving such that the flux into the page is decreasing, the induced field must point into the page.
The induced current therefore flows clockwise (as seen from the observer).
Summary Table
Situation
Change in Flux
Induced Magnetic Field
Direction of Induced Current (viewed from observer)
North pole of magnet moved towards coil
Increasing into page
Out of page
Anticlockwise
North pole of magnet moved away from coil
Decreasing into page
Into page
Clockwise
Loop rotating so area facing field decreases
Decreasing into page
Into page
Clockwise (for this orientation)
Loop rotating so area facing field increases
Increasing into page
Out of page
Anticlockwise (for this orientation)
Practical Implications
Understanding Lenz’s law is essential for:
Designing electric generators – the induced current opposes the motion, requiring mechanical input.
Braking systems in trains and roller coasters (eddy‑current brakes).
Protective devices such as circuit breakers and fuses, where induced currents can oppose fault currents.
Suggested diagram: A coil with a moving north‑pole magnet approaching from the left. Show magnetic field lines, direction of induced current (anticlockwise), and indicate the opposing magnetic field created by the induced current.
Key Take‑away
The induced e.m.f. always acts to oppose the change that produced it. This principle, expressed by Lenz’s law, is a direct consequence of the conservation of energy and is fundamental to all electromagnetic devices.