Magnetism and Electromagnetism

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Faraday\'s Electromagnetic Lab

Explore the simulation above to develop intuition for this topic.

1. Magnets and Magnetic Fields

1.1 Magnetic Materials

A magnet produces a magnetic field. It has two poles:

North-seeking pole (N): Points towards geographic north
South-seeking pole (S): Points towards geographic south

Rule: Like poles repel; unlike poles attract.

Magnetic materials: Iron, steel, nickel, and cobalt are attracted to magnets. Steel can be made Into a permanent magnet; iron is a soft magnetic material ( magnetised and demagnetised).

Induced magnetism: A magnetic material placed in a magnetic field becomes magnetised. The end Nearest to the north pole of the magnet becomes a south pole (attracted).

1.2 Why Induced Magnetism Causes Attraction

When an unmagnetised piece of iron is brought near a magnet, the magnetic domains within the iron Align with the external field. The end of the iron closest to the magnet’s north pole becomes a South pole, and the far end becomes a north pole. Since the south pole is closer to the magnet’s North pole, the attractive force is stronger than the repulsive force, and the net force is Attraction. When the magnet is removed, the domains in a soft magnetic material (iron) return to a Random orientation; in a hard magnetic material (steel), they remain aligned.

1.3 Magnetic Domains

A ferromagnetic material contains regions called domains, each of which behaves like a tiny Magnet. In an unmagnetised material, the domains are randomly oriented and their fields cancel. In a Magnetised material, the domains are aligned, producing a net magnetic field. The difference between Permanent magnets and temporary magnets is whether the domains remain aligned after the external Field is removed.

1.4 Magnetic Fields

A magnetic field is the region around a magnet where a magnetic force can be detected.

Magnetic field lines:

Go from north to south outside the magnet
Never cross
Closer lines indicate a stronger field
Point from north to south

1.5 Earth’s Magnetic Field

The Earth acts as a giant bar magnet. The geographic north pole is near the magnetic south pole (which is why the north pole of a compass points north — opposite poles attract).

The Earth’s magnetic field is generated by convection currents in the liquid iron outer core (the Geodynamo). This field extends far into space, forming the magnetosphere, which deflects charged Particles from the solar wind and protects the Earth from harmful cosmic radiation.

2. Electromagnetism

2.1 Magnetic Field of a Current-Carrying Wire

A straight wire carrying a current produces a circular magnetic field around it.

Right-hand grip rule: Grip the wire with your right hand, thumb pointing in the direction of Conventional current. Your fingers curl in the direction of the magnetic field.

2.2 Why a Current Creates a Magnetic Field

Moving charges produce magnetic fields. In a current-carrying wire, the conduction electrons are Moving, and their motion generates a magnetic field. This is a fundamental property of nature: the Magnetic field and the electric field are two aspects of the same electromagnetic phenomenon, as Described by Maxwell’s equations. You cannot have a magnetic field without moving charges (at least In classical physics).

2.3 The Motor Effect

When a current-carrying wire is placed in a magnetic field, it experiences a force. This is Called the motor effect.

Conditions for the force:

The wire must carry a current
The wire must be in a magnetic field
The wire must NOT be parallel to the magnetic field

Fleming’s Left-Hand Rule:

First finger (F): Field direction (N to S)
seCond finger (C): Current direction (conventional, + to -)
Thumb (T): Motion/force direction

Force on a conductor:

$F = BIl$

Where $F$ is force (N), $B$ is magnetic flux density (T, tesla), $I$ is current (A), and $l$ is the Length of conductor in the field (m).

Worked Example. A wire of length 0.15 m carries a current of 3 A in a magnetic field of flux Density 0.4 T. Calculate the force on the wire.

$F = BIl = 0.4 \times 3 \times 0.15 = 0.18 \mathrm{ N$

2.4 Why the Wire Must Not Be Parallel to the Field

The force on a current-carrying conductor in a magnetic field is given by $F = BIl\sin\theta$ Where $\theta$ is the angle between the current direction and the field direction. When $\theta = 0$ (wire Parallel to the field), $\sin\theta = 0$ and the force is zero. Maximum force occurs when $\theta = 90^{\circ}$ (wire perpendicular to the field). In GCSE, we assume the wire is Perpendicular unless stated otherwise.

2.5 Electric Motors

A DC motor uses the motor effect to produce continuous rotation.

Structure:

A coil of wire on an axle in a magnetic field
A split-ring commutator that reverses the current direction every half-turn
Carbon brushes that maintain electrical contact with the commutator

How it works:

Current flows through the coil in the magnetic field, producing a force
The forces on opposite sides of the coil act in opposite directions, causing rotation
The split-ring commutator reverses the current every half-turn, so the forces continue to produce rotation in the same direction

2.6 Why the Commutator Is Necessary

Without the commutator, the coil would rotate to the vertical position and then be pushed back (past It) in the opposite direction, oscillating rather than rotating continuously. The commutator Reverses the current at exactly the right moment (when the coil passes through the vertical), so That the force on each side of the coil always acts in the same rotational direction.

2.7 Factors Affecting Motor Speed

The speed of a DC motor depends on:

The current through the coil (higher current = greater force = faster rotation)
The strength of the magnetic field (stronger field = greater force)
The number of turns on the coil (more turns = greater total force)
The area of the coil (larger area = greater force per turn)

2.8 Electromagnets

An electromagnet is a coil of wire (solenoid) carrying a current. It produces a magnetic field When current flows and the field disappears when the current stops.

Magnetic field of a solenoid:

Inside the solenoid: the field is uniform and strong, running along the axis
Outside the solenoid: the field is similar to that of a bar magnet

Increasing the strength of an electromagnet:

Increase the current
Increase the number of turns on the coil
Use a soft iron core

Advantages over permanent magnets:

Can be switched on and off
Strength can be controlled by varying the current
Polarity can be reversed by reversing the current

Applications: Cranes for lifting scrap metal, electric bells, relay switches, MRI scanners, door Locks.

2.9 How a Relay Works

A relay is an electrically operated switch. A small current through the relay’s coil creates a Magnetic field that attracts an iron armature, closing (or opening) a set of contacts in a second Circuit. This allows a low-current circuit (e.g., a microcontroller output) to control a High-current circuit (e.g., a motor or heater) safely. The two circuits are electrically isolated From each other.

3. Electromagnetic Induction

3.1 Faraday’s Discovery

Electromagnetic induction is the generation of an electromotive force (EMF, potential Difference) across a conductor when it experiences a changing magnetic field.

Conditions for induction:

A conductor must move through a magnetic field, OR
The magnetic field through a coil must change

3.2 The Fundamental Principle

Electromagnetic induction is the converse of the motor effect. The motor effect converts electrical Energy into kinetic energy (current in a magnetic field produces motion). Electromagnetic induction Converts kinetic energy into electrical energy (motion in a magnetic field produces current). This Symmetry is not coincidental; it reflects the deep connection between electricity and magnetism.

3.3 Factors Affecting the Induced EMF

The size of the induced EMF is increased by:

Moving the magnet or conductor faster
Using a stronger magnet (greater magnetic flux density)
Increasing the number of turns on the coil
Increasing the area of the coil

3.4 Lenz’s Law

The direction of the induced current is such that it opposes the change that produced it.

This is a consequence of conservation of energy. If the induced current aided the change, it would Create energy from nothing. The induced current creates its own magnetic field that acts against the Change in the external field.

Example: If a north pole of a magnet is pushed into a coil, the induced current creates a Magnetic field that opposes the incoming north pole — the end of the coil nearest the magnet Becomes a north pole, repelling the magnet. If the magnet is pulled out, the current reverses to try To keep the magnet inside.

3.5 Generators (Alternators)

An AC generator converts kinetic energy into electrical energy using electromagnetic induction.

Structure:

A coil of wire that rotates in a magnetic field
Slip rings and brushes (instead of a split-ring commutator) so the contacts do not reverse

How it works:

As the coil rotates, the magnetic flux through it changes
This induces an EMF across the coil
Because the coil rotates, the EMF alternates (changes direction) — producing AC

Peak EMF:

$\mathrm{EMF_{\mathrm{peak} = NAB\omega$

Where $N$ is the number of turns, $A$ is the area of the coil, $B$ is the magnetic flux density, and $\omega$ is the angular velocity.

3.6 Why the Output Is AC

As the coil rotates, the rate of change of magnetic flux varies sinusoidally. When the coil is Perpendicular to the field, the flux through the coil is maximum but its rate of change is zero (the EMF is zero). When the coil is parallel to the field, the flux is zero but its rate of change is Maximum (the EMF is at its peak). This produces a sinusoidal output: the EMF varies as $V = V_0 \sin(\omega t)$ .

3.7 Difference Between a Motor and a Generator

Feature	Motor	Generator
Input energy	Electrical	Kinetic (mechanical)
Output energy	Kinetic (rotation)	Electrical
Contact	Split-ring commutator (reverses current)	Slip rings (maintains continuous contact)
Principle	Motor effect (current in field = force)	Electromagnetic induction (motion in field = EMF)

4. Transformers

4.1 Structure and Principle

A transformer changes the voltage of an alternating current supply. It consists of:

A primary coil (input)
A secondary coil (output)
A soft iron core that links the two coils magnetically

The alternating current in the primary coil produces a changing magnetic field in the iron core. This changing field induces an alternating EMF in the secondary coil.

4.2 Why Transformers Only Work with AC

A transformer requires a changing magnetic field to induce an EMF in the secondary coil. DC Produces a steady magnetic field once the current stabilises, so no EMF is induced. If you connect a Battery (DC) to a transformer, you get a brief pulse of EMF when you first connect it (as the Current rises from zero to its steady value), but then nothing. AC continuously changes direction, So the magnetic field continuously changes, and a continuous EMF is induced.

4.3 The Transformer Equation

For an ideal transformer (100% efficient):

$\frac{V_s}{V_p} = \frac{N_s}{N_p}$

Where $V_s$ and $V_p$ are the secondary and primary voltages, and $N_s$ and $N_p$ are the numbers of Turns on the secondary and primary coils.

Worked Example. A transformer has 200 turns on the primary coil and 50 turns on the secondary. The primary voltage is 240 V. Find the secondary voltage.

$\frac{V_s}{240} = \frac{50}{200} = \frac{1}{4}$ $V_s = 60 \mathrm{ V$

This is a step-down transformer.

4.4 Power in Transformers

For an ideal transformer, power in equals power out:

$V_p I_p = V_s I_s$

For a real transformer:

$V_s I_s = \eta \times V_p I_p$

Where $\eta$ is the efficiency ( 95—99% for large transformers).

4.5 Why Transformers in the National Grid Are So Efficient

Large transformers have efficiencies exceeding 99%. Losses occur due to:

Eddy currents: The changing magnetic field induces currents in the iron core, which heat it up. This is minimised by laminating the core (building it from thin, insulated sheets).
Hysteresis: The iron core is repeatedly magnetised and demagnetised, dissipating energy as heat. This is minimised by using soft iron, which magnetises and demagnetises .
Resistance of the coils: Current flowing through the copper coils produces heat ( $I^2R$ losses). This is minimised by using thick wire and keeping the coils short.
Flux leakage: Not all the magnetic flux from the primary coil links the secondary coil. This is minimised by using a closed core that provides a continuous magnetic path.

4.6 Transformers in the National Grid

Step-up transformers increase voltage at the power station:

Reduces current in the transmission cables
Reduces energy losses due to heating ( $P = I^2R$ )

Step-down transformers decrease voltage for safe domestic use:

From 400,000 V in transmission lines to 230 V for homes

5. The Generator Effect and Microphones

5.1 Dynamic Microphones

A dynamic microphone uses electromagnetic induction:

Sound waves cause a diaphragm to vibrate
The diaphragm is attached to a coil of wire in a magnetic field
The vibration of the coil induces an alternating current
The current varies with the sound wave, producing an electrical signal

5.2 Loudspeakers

A loudspeaker is essentially a motor working in reverse:

An alternating current flows through a coil in a magnetic field
The force on the coil causes it to vibrate
The coil is attached to a cone, which moves the air to produce sound waves

5.3 Induction Cooktops

An induction cooktop uses electromagnetic induction to heat a pan directly. A coil beneath the Ceramic surface carries a high-frequency alternating current, producing a rapidly changing magnetic Field. This field induces eddy currents in the base of the pan (which must be ferromagnetic), and The resistance of the pan material converts the eddy current energy into heat. The ceramic surface Itself does not heat up directly, making induction cooking more efficient and safer than gas or Conventional electric hobs.

6. Magnetic Flux and Flux Density (Higher Tier)

6.1 Magnetic Flux Density

The magnetic flux density $B$ is the force per unit current per unit length on a Current-carrying conductor perpendicular to the field:

$B = \frac{F}{Il}$

The unit is the tesla (T). A field of 1 T exerts a force of 1 N on a wire carrying 1 A with a length Of 1 m perpendicular to the field.

6.2 Magnetic Flux

The magnetic flux $\Phi$ through a coil of area $A$ perpendicular to a uniform field $B$ is:

$\Phi = BA$

The unit is the weber (Wb). When the coil is tilted at angle $\theta$ to the field:

$\Phi = BA\cos\theta$

Faraday’s law states that the induced EMF equals the negative rate of change of flux:

$\varepsilon = -N \frac{\Delta\Phi}{\Delta t}$

This is the mathematical expression of the observation that the induced EMF depends on how quickly The magnetic field changes, not on the absolute magnitude of the field.

Common Pitfalls

Using the wrong hand rule. Fleming’s LEFT-hand rule is for motors (force on a current-carrying wire). The RIGHT-hand grip rule is for the direction of the magnetic field around a wire.
Confusing generators and motors. Motors use current to produce motion; generators use motion to produce current.
Forgetting that transformers only work with AC. A changing magnetic field is required for induction; DC produces a constant field.
Reversing the transformer equation. The ratio $N_s/N_p$ equals $V_s/V_p$ Not $V_p/V_s$ .
Confusing magnetic and electric field lines. Magnetic field lines go from N to S; electric field lines go from + to -.
Forgetting that the motor effect requires the wire to NOT be parallel to the field. If the wire is parallel, the force is zero.
Confusing the north pole of a compass with geographic north. The north pole of a compass points towards geographic north, which means geographic north is near a magnetic south pole.
Stating that a magnet can be cut to isolate a single pole. Cutting a magnet in half produces two smaller magnets, each with a north and south pole. Magnetic monopoles have never been observed.
Forgetting that the force in $F = BIl$ is perpendicular to both the current and the field. The force, current, and field are mutually perpendicular.
Confusing the split-ring commutator (motor) with slip rings (generator). The commutator reverses the current every half-turn to maintain continuous rotation. Slip rings maintain continuous electrical contact without reversing.

Practice Questions

A wire of length 0.2 m carries a current of 5 A at right angles to a magnetic field of flux density 0.3 T. Calculate the force on the wire.
Explain the difference between a permanent magnet and an electromagnet. Give two advantages of each.
A transformer has 800 turns on its primary coil and 200 turns on its secondary coil. If the input voltage is 230 V, calculate the output voltage.
Describe how an AC generator produces an alternating current, explaining the role of the slip rings.
A student wants to increase the strength of an electromagnet. Describe three ways they could do this.
Calculate the current in the primary coil of a transformer that has a primary voltage of 240 V, a secondary voltage of 12 V, and a secondary current of 5 A. Assume 100% efficiency.
Explain why transformers are used in the National Grid, with reference to energy losses in transmission cables.
Use Fleming’s left-hand rule to determine the direction of the force on a wire carrying current into the page in a magnetic field pointing to the right.
Describe the difference between a motor and a generator in terms of energy transfers.
Explain why a transformer will not work with a DC supply.
A coil of 200 turns and area $0.01$ m $^2$ rotates at 50 Hz in a magnetic field of flux density 0.5 T. Calculate the peak EMF.
Explain the role of the iron core in a transformer. Why is the core laminated?
A wire of length 0.3 m carries a current of 4 A at an angle of $30^{\circ}$ to a magnetic field of flux density 0.6 T. Calculate the force on the wire.
Describe how Lenz’s law is a consequence of the principle of conservation of energy.
A step-down transformer converts 230 V to 12 V. If the primary coil has 460 turns and the secondary coil has 24 turns, and the transformer is 96% efficient, calculate the secondary current when the primary current is 0.5 A.

7. Worked Example: Transformer Power and Efficiency

A step-down transformer converts $230 \mathrm{ V$ to $12 \mathrm{ V$ . The primary coil has 920 turns. A device connected to the secondary draws $5 \mathrm{ A$ at $12 \mathrm{ V$ . The transformer is 95% Efficient.

Step 1: Find the number of secondary turns.

$\frac{N_s}{N_p} = \frac{V_s}{V_p} \implies N_s = 920 \times \frac{12}{230} = 48 \mathrm{ turns$

Step 2: Calculate the power delivered to the load.

$P_s = V_s I_s = 12 \times 5 = 60 \mathrm{ W$

Step 3: Calculate the power drawn from the primary.

$P_p = \frac{P_s}{\eta} = \frac{60}{0.95} = 63.2 \mathrm{ W$

Step 4: Calculate the primary current.

$I_p = \frac{P_p}{V_p} = \frac{63.2}{230} = 0.275 \mathrm{ A$

Step 5: Power wasted.

$P_{\mathrm{wasted} = P_p - P_s = 63.2 - 60 = 3.2 \mathrm{ W$

8. Derivation: Faraday’s Law from the Definition of Magnetic Flux

Faraday’s law states that the induced EMF equals the rate of change of magnetic flux linkage:

$\varepsilon = -N\frac{\Delta\Phi}{\Delta t}$

Physical argument: Consider a coil of $N$ turns in a changing magnetic field. The magnetic flux $\Phi = BA\cos\theta$ through each turn is changing. The total flux linkage is $N\Phi$ . If the flux Changes by $\Delta\Phi$ in time $\Delta t$ The rate of change is $\Delta\Phi / \Delta t$ And the Induced EMF is proportional to this rate. The negative sign (Lenz’s law) indicates that the induced EMF opposes the change in flux.

Quantitative example: A coil of 200 turns and area $0.02 \mathrm{ m^2$ is in a magnetic field of Flux density $0.5 \mathrm{ T$ . The field is reduced to zero in $0.05 \mathrm{ s$ .

$\Delta\Phi = BA = 0.5 \times 0.02 = 0.01 \mathrm{ Wb$

$\varepsilon = N\frac{\Delta\Phi}{\Delta t} = 200 \times \frac{0.01}{0.05} = 200 \times 0.2 = 40 \mathrm{ V$

9. Why Lenz’s Law Is a Consequence of Conservation of Energy

If the induced current aided the change in flux (instead of opposing it), a small change in the Magnetic field would produce an induced current that further increased the change, producing more Current, and so on. This would create energy from nothing — a perpetual motion machine of the first Kind. The fact that the induced current opposes the change ensures that energy must be supplied to Maintain the changing flux. The work done against the opposing force is converted into electrical Energy.

10. Worked Example: Force on a Wire at an Angle

A wire of length $0.25 \mathrm{ m$ carries a current of $4 \mathrm{ A$ at an angle of $30^{\circ}$ to A magnetic field of flux density $0.6 \mathrm{ T$ . Calculate the force on the wire.

$F = BIl\sin\theta = 0.6 \times 4 \times 0.25 \times \sin 30^{\circ}$

$= 0.6 \times 4 \times 0.25 \times 0.5 = 0.3 \mathrm{ N$

If the wire were perpendicular to the field ( $\theta = 90^{\circ}$ ), the force would be $0.6 \mathrm{ N$ — twice as large. At $\theta = 0^{\circ}$ (parallel), the force would be zero.

11. The Right-Hand Rule vs Fleming’s Left-Hand Rule

Students often confuse these two rules. Here is a clear distinction:

Rule	Used For	What It Finds
Right-hand grip rule	Finding the direction of the magnetic field around a current-carrying wire	Field direction (fingers curl in field direction)
Fleming’s left-hand rule	Finding the direction of the force on a current-carrying wire in a magnetic field	Force direction (thumb)
Right-hand rule (general)	Finding the direction of the magnetic field produced by a current loop or solenoid	North pole direction

The right-hand grip rule has nothing to do with the motor effect. It tells you the shape of the Magnetic field around a wire. Fleming’s left-hand rule tells you the direction of the force when you Already know the field direction and the current direction.

12. Worked Example: Electromagnet Design

Design an electromagnet that can lift a $2 \mathrm{ kg$ steel block. The electromagnet has a soft Iron core and 500 turns of wire. The minimum force required is $F = mg = 2 \times 9.8 = 19.6 \mathrm{ N$ .

The force on the steel block depends on the magnetic field produced by the electromagnet. For a Simple solenoid, the magnetic flux density at the centre is approximately:

$B = \frac{\mu_0 n I}{L}$

Where $n$ is the number of turns per unit length and $L$ is the length of the solenoid. Without more Details of the geometry, we can use the practical approach: the force is proportional to $NI$ (current times turns). Doubling either the current or the number of turns doubles the magnetic Force.

Key design considerations:

Use a soft iron core ( magnetised and demagnetised)
Maximise the number of turns (increases field proportionally)
Maximise the current (limited by the power supply and wire heating)
Ensure good thermal contact between the core and the block

13. Comparing Motors and Generators: A Deeper Look

Both motors and generators involve a coil rotating in a magnetic field. The difference is the Direction of energy conversion:

Aspect	Motor	Generator
Energy in	Electrical	Mechanical (kinetic)
Energy out	Mechanical (kinetic)	Electrical
Contact	Split-ring commutator	Slip rings
Current direction	Reverses every half-turn	Alternates
Output	Continuous rotation	Alternating EMF

The split-ring commutator in a motor ensures that the current always flows in the correct direction To produce a torque that maintains rotation. In a generator, the slip rings maintain continuous Contact with the coil without reversing, so the AC produced by the rotating coil is transmitted Directly to the external circuit.

14. Worked Example: AC Generator Peak EMF

A coil of 100 turns and area $0.03 \mathrm{ m^2$ rotates at 50 Hz in a magnetic field of flux density $0.4 \mathrm{ T$ . Calculate the peak EMF.

$\mathrm{EMF_{\mathrm{peak} = NAB\omega = NAB \times 2\pi f$

$= 100 \times 0.03 \times 0.4 \times 2\pi \times 50$

$= 100 \times 0.03 \times 0.4 \times 314.16$

$= 376.99 \mathrm{ V \approx 377 \mathrm{ V$

The RMS voltage would be $377 / \sqrt{2} \approx 267 \mathrm{ V$ .

15. Magnetic Materials: Hard vs Soft

Property	Soft Magnetic Material	Hard Magnetic Material
Examples	Iron, mild steel	Steel, alnico, neodymium
Ease of magnetisation	Easy	Hard
Retention of magnetism	Loses it	Retains it permanently
Use	Electromagnet cores, transformers	Permanent magnets, motors
Hysteresis loss	Low	High

The distinction is critical for applications. A transformer core must be made of soft iron so that It can be magnetised and demagnetised rapidly by the alternating current without significant energy Loss. A permanent magnet in a motor must be made of a hard magnetic material so that it retains its Magnetism despite the changing fields produced by the motor’s coils.

16. Practice Questions (Additional)

An electromagnet has 300 turns and carries a current of $3 \mathrm{ A$ . The magnetic flux density at its centre is $0.15 \mathrm{ T$ . If the current is increased to $5 \mathrm{ A$ and the number of turns is increased to 600, calculate the new flux density.
Explain, with reference to Lenz’s law, why a magnet dropped through a copper tube falls more slowly than through a plastic tube.
A transformer has 1000 turns on its primary and 50 turns on its secondary. The primary is connected to $230 \mathrm{ V$ mains. If the secondary current is $8 \mathrm{ A$ and the transformer is 92% efficient, calculate the primary current.
Describe how you would demonstrate the motor effect in a school laboratory. Include a diagram description and explain how to reverse the direction of the force.
A wire carrying a current of $6 \mathrm{ A$ is placed at right angles to a magnetic field. The force on the wire is $0.72 \mathrm{ N$ when the wire is $0.3 \mathrm{ m$ long. Calculate the magnetic flux density.
Explain why transformers are essential for the efficient distribution of electrical energy from power stations to consumers. Include quantitative reasoning.
A rectangular coil of 200 turns, dimensions $5 \mathrm{ cm \times 8 \mathrm{ cm$ Rotates at $40 \mathrm{ Hz$ in a magnetic field of flux density $0.5 \mathrm{ T$ . Calculate (a) the peak EMF and (b) the EMF when the coil makes an angle of $60^{\circ}$ with the field.
Compare and contrast permanent magnets and electromagnets. Give two specific applications where each is preferred.
A student investigates how the number of turns on an electromagnet affects the strength of the magnetic field. Describe a suitable method, identify the independent, dependent, and control variables, and explain how the results should be analysed.
Explain why the core of a transformer is laminated. What would happen if the core were made from a single solid piece of iron?

Extended Worked Examples

Example 26: Electromagnetic Induction Quantitative

A coil of 200 turns is placed in a magnetic field. The magnetic flux through the coil changes from $0.02 \mathrm{ Wb$ to $0.08 \mathrm{ Wb$ in $0.05 \mathrm{ s$ . Calculate the average EMF induced.

Step 1: Calculate the change in flux linkage

$\Delta(N\Phi) = N\Delta\Phi = 200 \times (0.08 - 0.02) = 200 \times 0.06 = 12 \mathrm{ Wb turns$

Step 2: Apply Faraday’s law

$\varepsilon = -\frac{\Delta(N\Phi)}{\Delta t} = -\frac{12}{0.05} = -240 \mathrm{ V$

The magnitude is $240 \mathrm{ V$ (the minus sign indicates direction via Lenz’s law).

Example 27: National Grid Power Loss Comparison

A power station generates $500 \mathrm{ MW$ of power. Compare the power loss in the transmission Cables if the power is transmitted at (a) $25 \mathrm{ kV$ and (b) $400 \mathrm{ kV$ Given a cable Resistance of $2 \Omega$ .

Step 1: At $25 \mathrm{ kV$

$I = \frac{P}{V} = \frac{500 \times 10^6}{25 \times 10^3} = 20000 \mathrm{ A$

$P_{\mathrm{loss} = I^2 R = (20000)^2 \times 2 = 8 \times 10^8 \mathrm{ W = 800 \mathrm{ MW$

This is more than the generated power! The system is completely impractical at this voltage.

Step 2: At $400 \mathrm{ kV$

$I = \frac{500 \times 10^6}{400 \times 10^3} = 1250 \mathrm{ A$

$P_{\mathrm{loss} = (1250)^2 \times 2 = 3.125 \times 10^6 \mathrm{ W = 3.125 \mathrm{ MW$

This is only $0.625\%$ of the generated power.

Step 3: Efficiency comparison

At $25 \mathrm{ kV$ : $\eta = \frac{500 - 800}{500} \times 100 = \mathrm{negative (impossible)$

At $400 \mathrm{ kV$ : $\eta = \frac{500 - 3.125}{500} \times 100 = 99.375\%$

:::info Step-up transformers increase the voltage (and decrease the current) for transmission, Dramatically reducing $I^2R$ losses. Step-down transformers then reduce the voltage to safe levels For domestic use. This is the fundamental reason the National Grid uses high-voltage transmission.

Example 28: Designing an Electromagnet

Design an electromagnet that can lift a $5 \mathrm{ kg$ steel block. The electromagnet has a soft Iron core, 500 turns of wire, and operates from a $12 \mathrm{ V$ DC supply. Determine the required Current.

Step 1: Force needed

$F = mg = 5 \times 9.8 = 49 \mathrm{ N$

Step 2: Magnetic field strength needed

For a rough estimate, the force on a magnetic material near an electromagnet is approximately:

$F \approx \frac{B^2 A}{2\mu_0}$

Assuming the pole face area is $A = 0.005 \mathrm{ m^2$ ( $50 \mathrm{ cm^2$ ):

$49 = \frac{B^2 \times 0.005}{2 \times 4\pi \times 10^{-7}}$

$B^2 = \frac{49 \times 2.513 \times 10^{-6}}{0.005} = 0.02463$

$B = 0.157 \mathrm{ T$

Step 3: Current required (solenoid approximation)

$B = \mu_0 \frac{NI}{L}$

Assuming the solenoid length is $L = 0.2 \mathrm{ m$ :

$0.157 = 4\pi \times 10^{-7} \times \frac{500 \times I}{0.2}$

$I = \frac{0.157 \times 0.2}{4\pi \times 10^{-7} \times 500} = \frac{0.0314}{6.283 \times 10^{-4}} = 50 \mathrm{ A$

This is a very high current. In practice, we would increase the number of turns or reduce the air Gap to achieve the required field with a more practical current.

Common Pitfalls Extended

Pitfall 6: Confusing Magnetic Field Lines with Electric Field Lines

Magnetic field lines form closed loops (they have no beginning or end). Electric field lines start On positive charges and end on negative charges. This is a consequence of the fact that there are no Magnetic monopoles (isolated north or south poles).

Pitfall 7: Getting the Transformer Equation Wrong

The transformer equation is $\frac{V_s}{V_p} = \frac{N_s}{N_p}$ . The voltage ratio equals the turns ratio. A common error is to invert this or to use current instead of voltage. For current, The relationship is inverted: $\frac{I_s}{I_p} = \frac{N_p}{N_s}$ .

Pitfall 8: Forgetting That Lenz’s Law Is About Conservation of Energy

Lenz’s law states that the induced current opposes the change that causes it. This is not just a Direction rule — it is a consequence of conservation of energy. If the induced current aided the Change, it would create energy from nothing, violating the first law of thermodynamics.

Additional Practice Problems

A transformer has 1000 turns on the primary and 50 turns on the secondary. The primary is connected to $230 \mathrm{ V$ AC. Calculate the secondary voltage and the primary current when the secondary delivers $10 \mathrm{ A$ to a load.
A wire carrying $5 \mathrm{ A$ is placed at right angles to a magnetic field of flux density $0.3 \mathrm{ T$ . The length of wire in the field is $0.15 \mathrm{ m$ . Calculate the force on the wire and state the direction using Fleming’s left-hand rule.
Explain how a loudspeaker works, including the role of the permanent magnet, the coil, and the alternating current. Why does the cone vibrate at the frequency of the AC signal?
A student investigates how the strength of an electromagnet varies with current. Describe a suitable method, including how to measure the magnetic field strength and how to ensure a fair test.
Explain why transformers only work with AC and not DC. What would happen if you connected a transformer to a DC supply?

Practice Problems

Question 1: Electromagnetic induction

A bar magnet is pushed into a coil of wire connected to a galvanometer. Describe what happens to the galvanometer needle and explain why. What happens if the magnet is held stationary inside the coil?

Answer

The galvanometer needle deflects. As the magnet moves into the coil, the magnetic flux through the coil changes. According to Faraday’s law, a changing magnetic flux induces an electromotive force (EMF) in the coil, causing a current to flow. The needle returns to zero when the magnet is held stationary because there is no change in magnetic flux, so no EMF is induced.

Question 2: Transformer calculation

A step-down transformer has 2000 turns on the primary coil and 100 turns on the secondary coil. The primary voltage is $240 \mathrm{ V$ . Calculate the secondary voltage and explain why the transformer is described as step-down.

Answer

$\frac{V_p}{V_s} = \frac{N_p}{N_s}$ So $V_s = V_p \times \frac{N_s}{N_p} = 240 \times \frac{100}{2000} = 12 \mathrm{ V$ .

It is a step-down transformer because the secondary voltage ( $12 \mathrm{ V$ ) is lower than the primary voltage ( $240 \mathrm{ V$ ). There are fewer turns on the secondary coil than the primary.

Question 3: Motor effect

Explain how a DC motor works. Describe the role of the split-ring commutator.

Answer

A current-carrying coil in a magnetic field experiences a force (motor effect). The force on opposite sides of the coil acts in opposite directions, causing the coil to rotate. The split-ring commutator reverses the direction of current in the coil every half-turn, ensuring that the forces always act in the same rotational direction, so the coil continues to spin.

Question 4: Magnetic field of a wire

Describe the magnetic field pattern around a straight current-carrying wire. Explain how you would use the right-hand grip rule to determine the direction of the field.

Answer

The magnetic field consists of concentric circles centred on the wire. The field is strongest close to the wire and weakens with distance.

Right-hand grip rule: grip the wire with your right hand, with your thumb pointing in the direction of conventional current. Your fingers curl in the direction of the magnetic field lines.

Question 5: Uses of electromagnets

Describe how an electromagnet works and give two examples of its use in everyday devices.

Answer

An electromagnet is a coil of wire (solenoid) wrapped around an iron core. When current flows through the coil, a magnetic field is produced. The iron core becomes magnetised by induction, greatly strengthening the magnetic field. When the current is switched off, the iron loses most of its magnetism.

Examples: (1) Electric bells — the electromagnet attracts a metal striker. (2) Scrap yard cranes — the electromagnet picks up and releases metal objects. (3) Relays in circuits.

Worked Examples

Example 1:

A typical exam question on Magnetism and Electromagnetism requires you to apply your knowledge to an unfamiliar context. Read the question carefully, identify the key concept being tested, and structure your answer using the appropriate terminology.

Example 2:

Multi-step problems in Magnetism and Electromagnetism often combine two or more concepts. Break the problem down: identify what you need to find, recall the relevant formula or principle, substitute values, and state your answer with correct units or formatting.

Summary

This topic covers the fundamental principles of magnetism and electromagnetism, including the key equations, experimental methods, and applications relevant to the specification.

Key concepts include:

gravitational fields and potential
electric fields and Coulomb’s law
capacitance
magnetic fields and the motor effect
electromagnetic induction

A strong understanding of these principles, combined with regular practice of quantitative problems and past paper questions, is essential for success in examinations.

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