Grade 10

Advanced

9 min

Lesson 11 of 12

Electromagnetic Induction

Not Started

Explains how a changing magnetic field can generate an electric current.

What if you could generate electricity out of thin air just by moving a piece of metal? Every time you use a power outlet, you are using energy created by this exact 'magic'—the interaction between motion and magnetism.

Learning Objectives

1.Calculate magnetic flux and induced EMF using Faraday’s Law: $\epsilon = -N \frac{\Delta \Phi}{\Delta t}$
2.Predict the direction of induced current using Lenz’s Law and the principle of conservation of energy
3.Analyze how the number of turns, magnetic field strength, and speed of motion influence electrical output

The Foundation: Magnetic Flux

Before we can understand induction, we must define Magnetic Flux ( $\Phi$ ). Think of flux as the 'amount' of magnetic field passing through a specific area. It is calculated as $\Phi = B \cdot A \cdot \cos(\theta)$ , where $B$ is the magnetic field strength, $A$ is the area of the loop, and $\theta$ is the angle between the field and the normal to the surface. For induction to occur, this flux must change. If a magnet sits still inside a coil, the flux is high, but the change in flux is zero, resulting in no electricity. It is the delta ( $\Delta$ ) that creates the spark.

Quick Check

If you double the area of a wire loop while keeping the magnetic field constant, what happens to the magnetic flux?

Look at the formula

\Phi = B \cdot A \cdot \cos(\theta)

Answer

The magnetic flux doubles, as flux is directly proportional to the area ( $A$ ).

Faraday’s Law of Induction

Michael Faraday discovered that the Induced EMF (Electromotive Force, or voltage) is directly proportional to the rate at which the magnetic flux changes. The formula is:

\epsilon = -N \frac{\Delta \Phi}{\Delta t}

Here,

N

represents the number of turns in the wire coil. This equation tells us three ways to increase voltage: increase the number of loops, use a stronger magnet (increase

\Delta B

), or move the magnet faster (decrease

\Delta t

). The negative sign, however, holds a deeper secret known as Lenz's Law.

A coil with $N = 50$ turns experiences a change in magnetic flux of $0.02\text{ Wb}$ over a period of $0.1\text{ seconds}$ . Calculate the induced EMF.

1. Identify the variables: $N = 50$ , $\Delta \Phi = 0.02$ , $\Delta t = 0.1$ . 2. Apply Faraday's Law: $\epsilon = -50 \cdot \frac{0.02}{0.1}$ . 3. Calculate the result: $\epsilon = -50 \cdot 0.2 = -10\text{ V}$ . 4. The magnitude of the induced voltage is $10\text{ V}$ .

Lenz’s Law: Nature’s Resistance to Change

Lenz’s Law states that the direction of an induced current is always such that it creates a magnetic field that opposes the change in flux that produced it. Think of it as 'magnetic inertia.' If you push a North pole toward a coil, the coil will induce a current that creates its own North pole to push back. This isn't just a quirk of physics; it is required by the Law of Conservation of Energy. If the coil attracted the magnet instead, it would create energy out of nothing, violating the fundamental laws of the universe.

Quick Check

If a magnet's South pole is pulled away from a coil, what pole will the coil's induced current create on the side nearest the magnet?

Lenz's Law always acts to 'undo' the change.

Answer

A North pole, to try and attract the receding South pole and oppose the decrease in flux.

A bar magnet is dropped through a vertical copper pipe. Why does it fall slower than a regular rock?

1. As the magnet falls, the magnetic flux through the pipe changes. 2. This change induces Eddy Currents in the conductive copper pipe. 3. According to Lenz's Law, these currents create a magnetic field that opposes the magnet's motion. 4. This creates an upward magnetic force that counteracts gravity, causing the magnet to 'float' slowly downward.

A square loop of wire with side length $s = 0.1\text{ m}$ and resistance $R = 2\text{ }\Omega$ is pulled out of a uniform magnetic field $B = 0.5\text{ T}$ at a constant velocity $v = 2\text{ m/s}$ . Calculate the induced current.

1. The rate of change of area is $\frac{\Delta A}{\Delta t} = s \cdot v = 0.1 \cdot 2 = 0.2\text{ m}^2/\text{s}$ . 2. The induced EMF is $\epsilon = B \cdot \frac{\Delta A}{\Delta t} = 0.5 \cdot 0.2 = 0.1\text{ V}$ . 3. Using Ohm's Law ( $I = V/R$ ), the current $I = \frac{0.1}{2} = 0.05\text{ A}$ .

Key Takeaways

1Magnetic Flux ( $\Phi$ ) is the product of the magnetic field and the area it penetrates.
2Faraday's Law states that EMF is generated by the rate of change of flux, not the flux itself.
3Lenz's Law ensures the induced magnetic field always opposes the change in the original flux.
4To maximize induced voltage, increase the number of wire turns or the speed of the magnetic change.

Quick Check

Multiple Choice

Which of the following would NOT induce a current in a stationary wire loop?

Multiple Choice

If the time taken for a flux change is halved, what happens to the induced EMF?

True/False

Lenz's Law is essentially a manifestation of the Law of Conservation of Energy.

What's Next?

Review Tomorrow

In 24 hours, try to sketch a magnet entering a coil and use the Right-Hand Rule to determine the direction of the induced current based on Lenz's Law.

Practice Activity

Research how 'Regenerative Braking' in electric cars uses electromagnetic induction to recharge batteries when the car slows down.

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Electromagnetic Induction

Learning Objectives

The Foundation: Magnetic Flux

Faraday’s Law of Induction

Lenz’s Law: Nature’s Resistance to Change

Key Takeaways

Quick Check

What's Next?

Electromagnetic Induction

Learning Objectives

The Foundation: Magnetic Flux

Faraday’s Law of Induction

Lenz’s Law: Nature’s Resistance to Change

Key Takeaways

Quick Check

What's Next?