Physics (9702) | Electromagnetic induction

Electromagnetic Induction: Turning Magnetism into Electricity!

Welcome to one of the most exciting topics in Physics! Electromagnetic Induction is the fundamental principle behind how we generate almost all the electricity used globally. If you’ve ever wondered how a massive wind turbine or a simple phone charger works, this chapter holds the key.

Don't worry if it seems complicated—we will break down these ideas into simple, manageable steps, focusing on two key figures: Faraday (who figured out how much voltage is produced) and Lenz (who figured out the direction of that voltage).

1. Magnetic Flux (\(\Phi\)): Counting Field Lines

Before we can talk about inducing electricity, we need a way to measure the "amount" of magnetic field passing through an area. This is called Magnetic Flux.

1.1 Definition and Formula

Definition: Magnetic flux (\(\Phi\)) is defined as the product of the magnetic flux density (B) and the cross-sectional area (A) perpendicular to the direction of the magnetic flux density.

Think of magnetic flux like the amount of rain falling into a bucket. You need to know the strength of the rain (B) and the opening size of the bucket (A).

• Symbol: \(\Phi\) (Phi)
• Unit: The Weber (Wb).
  (Since \(\Phi = B \times A\), 1 Weber is equal to 1 Tesla square metre: \(1 \text{ Wb} = 1 \text{ T m}^{2}\))

The Key Formula for Magnetic Flux

The simplest form, when the area is perfectly perpendicular to the magnetic field lines:

\[\Phi = B A\]

Wait, what if the coil is tilted?

If the coil is tilted, the effective area that the field lines pass through decreases. We must always use the component of the area (or the component of B) that is perpendicular to the field lines.
In general, if \(\theta\) is the angle between the magnetic field lines (B) and the normal (perpendicular line) to the area (A), the formula is:

\[\Phi = B A \cos \theta\]

Tip: If the field lines are parallel to the plane of the coil (i.e., just skimming the side), \(\theta = 90^{\circ}\) and \(\cos 90^{\circ} = 0\). The flux is zero!

2. Magnetic Flux Linkage (\(N\Phi\))

In real-world applications, we don't just use one loop of wire; we use a coil with many turns.

2.1 Understanding Flux Linkage

Definition: Magnetic Flux Linkage (\(N\Phi\)) is the product of the magnetic flux (\(\Phi\)) passing through a single turn and the number of turns (N) in the coil.

If you have a coil with N turns, and the magnetic flux through one turn is \(\Phi\), the total flux linked is:

\[N\Phi = N B A\]

Analogy: If one loop of wire feels a magnetic pressure of 10 units, a coil with 100 loops feels a pressure of \(10 \times 100 = 1000\) units. This means you get a much bigger electrical effect!

Unit: Weber turns (Wb turns).

3. Faraday’s Law of Induction (Magnitude)

This is the core concept of electromagnetic induction. Michael Faraday discovered that if you want to generate an e.m.f. (voltage), you must change the magnetic environment.

3.1 State and Explanation of Faraday's Law

Faraday's Law: The magnitude of the induced electromotive force (e.m.f.) is directly proportional to the rate of change of magnetic flux linkage.

What does this really mean?

If you change the flux linkage very slowly, you get a small e.m.f. If you change it very rapidly, you get a large e.m.f.

The change in flux linkage, \(\Delta (N\Phi)\), can be caused by changing:

1. The magnetic flux density, B (e.g., moving a magnet faster).
2. The area of the coil exposed to the field, A (e.g., pulling a loop out of a field).
3. The angle, \(\theta\), between B and A (e.g., rotating a coil in a generator).
4. The number of turns, N (though usually fixed once the coil is built).

3.2 The Mathematical Formula

For calculations involving average e.m.f.:

\[E = \frac{\Delta (N\Phi)}{\Delta t}\]

Where:

• \(E\) is the magnitude of the induced e.m.f. (V)
• \(\Delta (N\Phi)\) is the change in flux linkage (Wb turns)
• \(\Delta t\) is the time taken for the change (s)

Key Takeaway from Faraday: The induced e.m.f. is NOT dependent on the absolute amount of flux, but only on how quickly the flux is changing.

Common Mistake Alert!

Students often confuse flux (\(\Phi\)) and rate of change of flux (\(\Delta \Phi / \Delta t\)). You can have a huge flux linkage, but if it is constant (not changing), the induced e.m.f. will be ZERO. For example, a magnet sitting stationary inside a coil creates flux, but no electricity.

4. Lenz's Law (Direction)

Faraday's law tells us *how much* e.m.f. is induced, but we need Lenz's Law to tell us *which way* the resulting current will flow.

4.1 State and Explanation of Lenz's Law

Lenz’s Law: The induced e.m.f. (and the resulting current) is always in such a direction as to oppose the change that produces it.

Analogy: Think of Lenz's Law as Physics telling the Universe, "I don't like change!"

• If you try to push a North pole into a coil, the coil will immediately generate a North pole on that side to push the magnet back out (i.e., oppose the movement).
• If you try to pull a North pole out of the coil, the coil will generate a South pole to try to pull it back in (i.e., oppose the decrease in flux).

This opposition is vital because it is a direct consequence of the conservation of energy. If the induced current *aided* the motion, you would create energy for free, which violates the law of conservation of energy! You must do work against the opposing force to induce the e.m.f.

4.2 Connecting Faraday and Lenz

In mathematical form, Lenz's Law is represented by the negative sign in Faraday's Law:

\[E = - \frac{\Delta (N\Phi)}{\Delta t}\]

The negative sign indicates that the induced e.m.f. acts to oppose the change in flux linkage.

4.3 Applying Lenz's Law (Step-by-Step)

To determine the direction of the induced current, you need to use a two-step process involving the Right-Hand Grip Rule:

1. Identify the Change: Is the magnetic flux increasing (e.g., magnet moving closer) or decreasing (e.g., magnet moving away)?
2. Determine the Opposition: The induced magnetic field must oppose this change.
   • If flux is increasing (pushing in N pole), the coil creates an opposing N pole.
   • If flux is decreasing (pulling out N pole), the coil creates an attracting S pole.
3. Use the Grip Rule: Once you know the pole created by the coil (N or S), point your right thumb in the direction of the induced North pole field, and your fingers will curl in the direction of the induced current.

5. Factors Affecting the Magnitude of Induced E.M.F.

Based on Faraday's Law, the magnitude of the induced e.m.f., \(E = \frac{\Delta (N\Phi)}{\Delta t}\), depends on these specific factors. These are often tested experimentally.

1. Rate of Change of Flux (\(1/\Delta t\)):
   • The faster the magnet moves, the greater the e.m.f. (Smaller \(\Delta t\)).
   • The faster the coil rotates (in a generator), the greater the e.m.f.
2. Magnetic Flux Density (B):
   • Using a stronger magnet (larger B) results in a greater e.m.f.
3. Number of Turns (N):
   • Using a coil with more turns (larger N) results in a greater e.m.f.
     (Remember the Flux Linkage concept: \(N\Phi\)).
4. Area (A) / Angle Change (\(\Delta \cos \theta\)):
   • Using a larger area coil, or changing the angle over a greater range (e.g., spinning 180 degrees instead of 90 degrees), increases the total change in flux, leading to a greater e.m.f.

The Dynamo Effect (Generators):

In an A.C. generator, a coil rotates at a constant angular speed (\(\omega\)) within a uniform magnetic field. The key is that the coil is constantly cutting magnetic field lines, causing a continuous change in flux linkage.

• When the plane of the coil is perpendicular to B (maximum flux linkage), the rate of change of flux is zero, so the induced e.m.f. is momentarily zero.
• When the plane of the coil is parallel to B (zero flux linkage), the coil is cutting lines at the fastest possible rate, so the induced e.m.f. is maximum.