Know that the direction of an induced e.m.f. opposes the change causing it

4.5.1 Electromagnetic Induction

Objective

Understand and apply Lenz’s law – the induced electromotive force (e.m.f.) always opposes the change that produces it.

Core Content Required by the Cambridge IGCSE 0625 Syllabus

• Two ways in which an e.m.f. can be induced (the only mechanisms required for the core syllabus).
• A simple laboratory experiment that demonstrates electromagnetic induction.
• Factors that affect the magnitude of the induced e.m.f.
• A qualitative description of Lenz’s law and a systematic method for determining the direction of the induced current.

How an e.m.f. Can Be Induced – The Two Mechanisms

These are the only two mechanisms that the IGCSE syllabus expects you to know:

1. Motion of a conductor in a static magnetic field – e.g. a rod sliding on parallel rails, a rectangular loop rotating in a uniform field.
2. Change of the magnetic field linking a stationary conductor – e.g. a bar‑magnet moved toward a fixed coil, or a solenoid whose current is varied.

Faraday’s Law (Quantitative Form)

The magnitude of the induced e.m.f. is proportional to the rate of change of magnetic flux \(\Phi\):

\[ \mathcal{E}= -\,\frac{\Delta\Phi}{\Delta t} \]

The negative sign is the mathematical statement of Lenz’s law – the induced e.m.f. acts so as to oppose the change in flux.

Lenz’s Law – Qualitative Form

When the magnetic flux through a closed loop changes, an induced current flows in a direction such that the magnetic field it creates opposes the original change in flux. This is a direct consequence of energy conservation.

Factors Affecting the Magnitude of the Induced e.m.f.

• Magnetic field strength (\(B\)) – stronger fields give larger \(\mathcal{E}\).
• Area of the loop (\(A\)) – a larger area intercepts more flux.
• Number of turns (\(N\)) – each turn contributes equally, so \(\mathcal{E}\) is multiplied by \(N\).
• Rate of change of flux – faster motion, higher frequency of rotation, or a rapidly varying external field increase \(\Delta\Phi/\Delta t\).

For a single loop rotating at angular speed \(\omega\) in a uniform field, the peak e.m.f. is

\[ \mathcal{E}_{\max}= N\,B\,A\,\omega \]

Worked Numerical Example

Calculate the maximum e.m.f. for a coil with the following data:

• Number of turns, \(N = 50\)
• Magnetic field, \(B = 0.20\;\text{T}\)
• Area of one turn, \(A = 0.010\;\text{m}^2\)
• Angular speed, \(\omega = 300\;\text{rad s}^{-1}\) (≈ 48 rev s\(^{-1}\))

Solution:

\[ \mathcal{E}_{\max}= 50 \times 0.20 \times 0.010 \times 300 = 50 \times 0.002 \times 300 = 50 \times 0.6 = 30\;\text{V} \]

The coil would produce a peak e.m.f. of 30 V.

Determining the Direction of the Induced e.m.f.

1. Identify the cause of the change (magnet moving, loop rotating, rod sliding, etc.).
2. Decide whether the magnetic flux through the circuit is increasing or decreasing.
3. Apply the right‑hand rule for generators:
   • Extend 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 direction in which the palm pushes (or the way the fingers curl) gives the direction of the induced conventional current (and therefore the e.m.f.) in the conductor.
4. Check the induced magnetic field produced by this current:
   • If it opposes the original change in flux, the direction is correct.
   • If not, reverse the current direction.

Simple Laboratory Demonstration of Electromagnetic Induction

Apparatus: coil (≈ 100 turns), galvanometer, bar magnet, ruler, stand, stopwatch.

Safety tip: Handle the magnet gently and keep the coil leads away from the galvanometer’s zero‑adjustment knob to avoid accidental damage.

Procedure:

1. Connect the coil to the galvanometer and zero the needle.
2. Place the magnet with its north pole facing the centre of the coil, about 2 cm away.
3. Rapidly push the magnet straight into the coil; observe and record the direction and magnitude of the needle deflection.
4. Pull the magnet out of the coil with the same speed; note the opposite deflection.
5. Measure the speed of insertion/removal (e.g., using a ruler and stopwatch) and repeat the experiment at different speeds. Record how the deflection changes – this links the observation to the “rate of change of flux” factor.
6. Optional: reverse the coil connections and verify that the direction of the induced current reverses.

This experiment clearly demonstrates that a changing magnetic flux induces an e.m.f., and that the induced current always opposes the change (Lenz’s law).

Worked Examples – Determining Direction

Example 1 – Magnet Approaching a Coil

• North pole moved toward a stationary coil → flux **into** the page is increasing.
• To oppose the increase, the induced field must point **out of** the page.
• Right‑hand rule gives an **anticlockwise** current when viewed from the magnet side.

Example 2 – Magnet Receding from a Coil

• North pole moved away → flux **into** the page is decreasing.
• Induced field must point **into** the page.
• Resulting current is **clockwise** (viewed from the magnet side).

Example 3 – Rotating a Rectangular Loop in a Uniform Field

• Loop rotates clockwise in a field directed **into** the page.
• When the area presented to the field decreases, the flux into the page decreases.
• Induced field therefore points **into** the page, giving a **clockwise** current as seen by the observer.

Summary Table – Direction of Induced Current

Situation	Change in Flux	Induced Magnetic Field	Direction of Induced Current (viewed from observer)
North pole moved toward coil	Increasing into page	Out of page	Anticlockwise
North pole moved away from coil	Decreasing into page	Into page	Clockwise
Loop rotating so that facing area decreases	Decreasing into page	Into page	Clockwise (for this orientation)
Loop rotating so that facing area increases	Increasing into page	Out of page	Anticlockwise (for this orientation)

Practical Implications of Lenz’s Law

• Electric generators – the induced current opposes the motion of the coil; mechanical work must be supplied to keep the coil turning.
• Eddy‑current brakes on trains and roller coasters use Lenz’s law to produce a retarding force without physical contact.
• Protective devices (circuit breakers, fuses) exploit induced currents that oppose fault currents, helping to interrupt them safely.

Key Take‑away

The induced e.m.f. always acts to oppose the change that produced it (Lenz’s law). This principle, expressed mathematically by the negative sign in Faraday’s law, underlies the operation of all electromagnetic devices and reflects the conservation of energy.