Electromagnetic Induction and Faraday's Law - Tenth Grade Science
In 1831, English physicist Michael Faraday made the foundational discovery that electricity could be generated from magnetism. He observed that whenever the magnetic flux linking a closed electrical conductor changes over time, an electric current is induced in the circuit. Known as electromagnetic induction, this phenomenon provides the working principle behind electric generators, induction cooktops, wireless charging systems, and the transformers that power electrical grids.
Faraday's Landmark Experiments
Faraday demonstrated electromagnetic induction through two classic experiments that established the relationship between motion, magnetism, and electricity.
FARADAY'S EXPERIMENT: MOVING MAGNET
Bar Magnet Moving IN Bar Magnet Moving OUT
[ N ][ S ] ====> <==== [ N ][ S ]
.---. .---.
/ \ / \
| Coil | | Coil |
\ / \ /
'---' '---'
| |
v v
( G ) Galvanometer ( G ) Galvanometer
Deflects RIGHT Deflects LEFT
Experiment 1: Relative Motion Between a Magnet and a Coil
Faraday connected a multi-turn coil of insulated wire to a sensitive center-zero galvanometer ($G$), with no battery in the circuit: When the north pole of a bar magnet was plunged into the interior of the coil, the galvanometer needle deflected momentarily to one side, indicating an induced current. When the magnet was held stationary inside the coil, the galvanometer returned to zero, showing that a static magnetic field produces no current. When the magnet was pulled out of the coil, the galvanometer deflected in the opposite direction, demonstrating that reversing the motion reverses the current. Plunging the magnet faster produced a larger deflection, confirming that the magnitude of the induced current depends on the rate of motion. Holding the magnet stationary while moving the coil yielded identical deflections, proving that relative motion between the conductor and the magnetic field is the governing factor.
FARADAY'S EXPERIMENT: MUTUAL INDUCTION
PRIMARY COIL (P) SECONDARY COIL (S)
+---------+ +---------+
| ( ( ( ( | | ) ) ) ) |
+----+----+ +----+----+
| |
Switch v
[/ ] ( G ) Galvanometer
| Deflects on MAKE
Battery and BREAK of switch
Experiment 2: Mutual Induction Between Two Stationary Coils
Faraday wound two separate coils of insulated copper wire onto a single iron core: Primary Coil ($P$): Connected in series with a DC battery and a tap key switch. Secondary Coil ($S$): Connected solely to a sensitive galvanometer.
Observations: At the instant the primary switch was closed, the galvanometer needle deflected momentarily before returning to zero. While a steady current flowed through the primary coil, the galvanometer remained at zero. At the instant the primary switch was opened, the galvanometer deflected momentarily in the opposite direction before returning to zero.
This experiment proved that physical mechanical motion is not strictly required. A changing current in the primary coil generates a changing magnetic field, which induces a current in the nearby secondary coil.
The Concept of Magnetic Flux
To quantify electromagnetic induction mathematically, we define the concept of magnetic flux ($\Phi$).
CONCEPT OF MAGNETIC FLUX
Magnetic Field Lines (B)
============================>
============================>
.-------.
/ \
| Area |
| (A) |
\ /
'-------'
Flux = Total lines passing through Area
Mathematical Definition
Magnetic flux ($\Phi$) represents the total count of magnetic field lines passing perpendicularly through a given surface area $A$. For a uniform magnetic field $B$ passing through a planar surface of area $A$ at an angle $\theta$ relative to the surface normal:
$$\Phi = B A \cos\theta$$
When the magnetic field lines pass perpendicular to the plane of the coil ($\theta = 0^\circ$), magnetic flux is maximized: $\Phi = B A$.
The SI Unit of Magnetic Flux: The Weber
The SI unit of magnetic flux is the weber, symbolized by $\text{Wb}$, named after the German physicist Wilhelm Weber. One weber represents the magnetic flux that, linking a circuit of one turn, produces an induced electromotive force of one volt when reduced to zero at a uniform rate over one second ($1 \text{ Wb} = 1 \text{ T}\cdot\text{m}^2 = 1 \text{ V}\cdot\text{s}$).
Faraday's Laws of Electromagnetic Induction
Faraday synthesized his experimental findings into two fundamental physical laws.
First Law (Qualitative)
Whenever the magnetic flux linking a closed electrical circuit changes over time, an electromotive force (EMF) is induced in the circuit. If the circuit is closed, this induced EMF produces an induced electric current. The induced EMF persists only while the magnetic flux continues to change.
Second Law (Quantitative)
The magnitude of the induced electromotive force ($\mathcal{E}$) in a circuit is directly proportional to the time rate of change of magnetic flux linking that circuit:
$$\mathcal{E} \propto \frac{\Delta \Phi}{\Delta t}$$
For a coil containing $N$ tightly wound turns:
$$\mathcal{E} = -N \frac{\Delta \Phi}{\Delta t} = -N \frac{\Phi_2 - \Phi_1}{t}$$
The negative sign in this equation reflects Lenz's Law.
Lenz's Law and Conservation of Energy
Formulated in 1834 by the Baltic German physicist Heinrich Lenz, Lenz's law specifies the direction of induced currents.
LENZ'S LAW MECHANISM
Pushing North Pole IN:
Coil face develops NORTH polarity to REPEL approach
[ N ] =====> ( N ) Coil Face
Anticlockwise current
Pulling North Pole OUT:
Coil face develops SOUTH polarity to ATTRACT retreat
<===== [ N ] ( S ) Coil Face
Clockwise current
Statement of Lenz's Law
Lenz's law states that the direction of an induced electric current is always such that its own magnetic field opposes the change in magnetic flux that produced it.
Physical Mechanism and Energy Conservation
When the north pole of a magnet is pushed toward a coil, the induced current flows in an anticlockwise direction, creating an induced North pole on the facing side of the coil. This induced North pole repels the incoming magnet. An external force must do mechanical work against this repulsion to move the magnet closer.
When the north pole is pulled away from the coil, the induced current reverses direction to clockwise, creating an induced South pole that attracts the receding magnet. Again, mechanical work must be done against this attraction.
This mechanical work done by an external agent is converted into electrical energy in the coil, satisfying the Law of Conservation of Energy. If the induced current did not oppose the motion, a slight push would cause the magnet to accelerate indefinitely on its own, generating infinite energy without input work—a physical impossibility.
Fleming's Right-Hand Rule (Generator Rule)
While Fleming's left-hand rule governs electric motors, Fleming's Right-Hand Rule determines the direction of induced current when a conductor moves across a magnetic field.
FLEMING'S RIGHT-HAND RULE
THUMB: Motion of Conductor (v)
^
|
| FOREFINGER: Magnetic Field (B)
| /
| /
|/
+-----------------> CENTER FINGER:
Induced Current (I)
All three digits held MUTUALLY PERPENDICULAR (90 deg)
Operational Statement
Stretch the thumb, forefinger, and center finger of your right hand mutually perpendicular to one another: Point the Forefinger in the direction of the Magnetic Field (from North to South). Point the Thumb in the direction of the mechanical Motion of the conductor. The outstretched Center Finger points in the direction of the Induced Current flowing through the conductor.
Chapter Exercises and Solutions
Exercise 1: A planar circular coil containing 500 turns of wire has a cross-sectional area of $0.020 \text{ m}^2$. It is placed perpendicular to a uniform magnetic field of 0.40 teslas. If the magnetic field is reduced to zero at a uniform rate over a duration of 0.050 seconds, calculate the initial magnetic flux linking the coil, the rate of change of flux, and the magnitude of the induced electromotive force.
Solution 1: The initial magnetic flux linking a single turn of the coil is $\Phi_1 = B A = 0.40 \text{ T} \times 0.020 \text{ m}^2 = 0.0080 \text{ Wb}$. When the field collapses to zero, the final flux is $\Phi_2 = 0$. The change in magnetic flux per turn is $\Delta \Phi = \Phi_2 - \Phi_1 = 0 - 0.0080 \text{ Wb} = -0.0080 \text{ Wb}$. The rate of change of magnetic flux is $\Delta \Phi / \Delta t = -0.0080 \text{ Wb} / 0.050 \text{ s} = -0.16 \text{ Wb/s}$. According to Faraday's quantitative law, the induced electromotive force in a coil of $N = 500$ turns is $\mathcal{E} = -N (\Delta \Phi / \Delta t) = -500 \times (-0.16 \text{ Wb/s}) = +80.0 \text{ V}$. An electromotive force of 80 volts is induced across the terminals of the coil.
Exercise 2: A bar magnet is dropped vertically downward through a hollow, stationary copper pipe. Explain why the falling magnet reaches a constant terminal velocity and falls more slowly than an identical non-magnetic brass weight dropped down the same pipe.
Solution 2: As the bar magnet falls through the conductive copper pipe, its moving magnetic field causes a continuously changing magnetic flux in the circular wall sections of the pipe above and below it. According to Faraday's law, this changing flux induces circular eddy currents in the copper walls. By Lenz's law, these induced currents flow in directions that oppose the magnet's motion: the copper pipe section immediately below the falling magnet develops a repulsive magnetic polarity, while the section above develops an attractive magnetic polarity. Both sections exert upward retarding magnetic forces on the falling magnet. As the magnet accelerates, these upward braking forces increase until they balance the downward gravitational force ($F_{\text{drag}} = m g$). Once balanced, the magnet falls at a steady terminal velocity. The non-magnetic brass weight produces no changing magnetic flux, induces no currents, experiences no magnetic drag, and accelerates freely under gravity ($g$).
Exercise 3: Contrast Fleming's Left-Hand Rule with Fleming's Right-Hand Rule, identifying which physical machine each rule applies to and distinguishing the cause from the effect in both cases.
Solution 3: Fleming's Left-Hand Rule applies to electric motors, where electrical energy is converted into mechanical kinetic motion. In the left-hand rule, the magnetic field (forefinger) and the supplied electric current (center finger) are the inputs or causes, while the resulting mechanical force or motion (thumb) is the physical output or effect. In contrast, Fleming's Right-Hand Rule applies to electric generators, where mechanical energy is converted into electrical energy via electromagnetic induction. In the right-hand rule, the magnetic field (forefinger) and the applied mechanical motion (thumb) are the inputs or causes, while the resulting induced electric current (center finger) is the generated output or effect.