Grade 11 Physical Sciences
Term 2 · Weeks 2–3

Electromagnetism

Paper 1 — Physics · Grade 11

Electricity and magnetism are two aspects of a single fundamental force. A current-carrying conductor produces a magnetic field; a changing magnetic field induces an emf in a conductor. These two discoveries — Oersted's (1820) and Faraday's (1831) — underpin every electric motor and generator on Earth.

Week 2

4.1 Magnetic Fields Around Current-Carrying Conductors

Describe the magnetic field around a current-carrying conductor using the right-hand rule.Describe the magnetic field of a solenoid and identify the N and S poles.

In 1820 Hans Christian Oersted discovered that a wire carrying an electric current deflects a nearby compass needle. This proved that an electric current produces a magnetic field. The field exists in a plane perpendicular to the wire and forms concentric circles around it. The DIRECTION of the field depends on the direction of the current.

THE RIGHT-HAND RULE for a straight conductor: Point the thumb of your right hand in the direction of the conventional current (from + to −). Your fingers curl in the direction of the magnetic field lines around the wire. Above the wire the field points out of the page (toward you); below the wire it points into the page.

I (current up)B (field)Right-hand rule: thumb → I, fingers curl → B• (toward you)
Figure 4.1 — Cross-sections of a current-carrying wire. Left: current coming OUT of the page (dot ·) — field circles anti-clockwise. Right: current going INTO the page (cross ×) — field circles clockwise. The field strength decreases with distance from the wire.
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Exam Tip

EXAM TIP — In diagrams, a circle with a dot (⊙) means current or field coming OUT of the page toward you (think the tip of an arrow). A circle with a cross (⊗) means current or field going INTO the page away from you (think the tail feathers of an arrow). Learn these symbols — they appear in nearly every electromagnetism question.

A SOLENOID is a long coil of wire wound in a helix. When current flows through the solenoid, the magnetic fields of each individual loop add together to produce a strong, nearly uniform magnetic field inside the coil. The field pattern outside the solenoid is almost identical to that of a bar magnet — with a North pole at one end and a South pole at the other.

NSField lines run S→N inside; N→S outside (like a bar magnet)
Figure 4.2 — Magnetic field of a solenoid. Inside the solenoid the field lines are parallel and uniform (strong field). Outside, the field lines curve from N to S, just like a bar magnet. The right-hand rule for a solenoid: wrap the right hand around the solenoid with fingers pointing in the direction of conventional current — the thumb points toward the North pole.
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Note

RIGHT-HAND RULE FOR THE SOLENOID: Curl the fingers of the right hand in the direction of the conventional current flowing around the coil. The extended thumb points toward the NORTH pole of the solenoid. Reversing the current reverses the poles.

Solenoid vs Bar Magnet

PropertySolenoid (current-carrying coil)Bar Magnet
Field patternIdentical outside — field lines from N to SSame external field pattern
Can poles be reversed?Yes — reverse the current directionNo — poles are fixed by the material
Field strength adjustable?Yes — increase current or number of turnsNo — fixed by the permanent magnet
ApplicationsElectromagnets, electric motors, relaysCompasses, fridge magnets, speakers
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Practice Question

A solenoid is connected to a battery so that conventional current flows from left to right along the top of the coil. (a) Using the right-hand rule, identify which end of the solenoid is the North pole. (b) How would you increase the strength of the magnetic field inside the solenoid without changing the current? (c) What happens to the poles if the battery terminals are reversed?

(6 marks)

Week 2

4.2 Faraday's Law and Lenz's Law

State Faraday's law of electromagnetic induction.Explain Lenz's law.

In 1831 Michael Faraday discovered that a changing magnetic field through a loop of wire induces (creates) an emf in the loop. This is the principle of ELECTROMAGNETIC INDUCTION and it is the foundation of electrical generators. The key word is CHANGING — a static (unchanging) magnetic field produces no emf.

Definition

Faraday's Law

The emf induced around a loop of conductor is directly proportional to the rate of change of magnetic flux through the area enclosed by the loop. Mathematically: emf = −N(ΔΦ/Δt), where N is the number of turns and ΔΦ/Δt is the rate of change of flux. The negative sign expresses Lenz's law (the induced current opposes the change causing it).

Formula

Faraday's Law of Electromagnetic Induction

E=−NΔΦΔt\mathcal{E} = -N\frac{\Delta\Phi}{\Delta t}

E = induced emf (V), N = number of turns in the coil, Δφ = change in magnetic flux (Wb), Δt = time interval (s), φ = B·A where B = magnetic field strength (T) and A = area of loop (m²)

SI unit: V (volt)

Formula

Magnetic flux

Φ=BAcos⁡θ\Phi = BA\cos\theta

φ = magnetic flux (Wb), B = magnetic field strength (T), A = area of the loop perpendicular to the field (m²)

SI unit: Wb (weber)

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Watch Out

COMMON MISTAKE — The emf is induced by a CHANGE in flux, NOT by the flux itself. If B is constant and the coil is stationary, Δφ = 0 and E = 0, even if the field is very strong. Flux must be changing for an emf to be induced.

Loop (N turns)NSmoving →GChanging flux → induced emf: ε = −NΔφ/ΔtLenz's law: induced current opposes change
Figure 4.3 — Faraday's law demonstrated. As a bar magnet moves toward a coil (left), the magnetic flux through the coil increases, inducing an emf. The galvanometer deflects. When the magnet is stationary (middle), flux is constant, emf = 0. When the magnet moves away (right), flux decreases and the emf is induced in the opposite direction.

LENZ'S LAW gives the direction of the induced current. It states: the induced current flows in a direction that opposes the change that caused it. In practice: if a North pole of a magnet moves toward a coil, the induced current creates a magnetic field that opposes the approaching North pole — so the near face of the coil also becomes a North pole (repelling). If the magnet is moving away, the near face becomes a South pole (attracting, opposing the withdrawal).

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Note

LENZ'S LAW and energy conservation: Lenz's law is a consequence of the law of conservation of energy. If the induced current aided the change that caused it, that change would be self-sustaining — which would create energy from nothing. The opposition ensures you must do work to change the flux.

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Exam Tip

EXAM TIP — The negative sign in E = −N(Δφ/Δt) represents Lenz's law mathematically. In South African matric exams, you are expected to state Lenz's law in words and use it to determine the direction of the induced current.

Worked Example

A coil of 200 turns has a cross-sectional area of 0,05 m². A uniform magnetic field perpendicular to the coil changes from 0,4 T to 1,2 T in 0,5 s. Calculate the magnitude of the induced emf.

Given

  • N = 200 turns
  • A = 0,05 m²
  • B₁ = 0,4 T
  • B₂ = 1,2 T
  • Δt = 0,5 s

Find

|E| = ?

Solution

  1. 1Calculate Δφ = ΔB × A = (B₂ − B₁) × A
  2. 2Δφ = (1,2 − 0,4) × 0,05 = 0,8 × 0,05 = 0,04 Wb
  3. 3|E| = N × |Δφ/Δt|
  4. 4|E| = 200 × (0,04 / 0,5)
  5. 5|E| = 200 × 0,08 = 16 V
Answer: |E| = 16 V
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Practice Question

A single-turn coil of area 0,02 m² is placed perpendicular to a magnetic field. The field increases from 0 T to 0,6 T in 0,3 s. (a) Calculate the induced emf. (b) State whether the induced current opposes or assists the increase in flux. Give a reason.

(6 marks)

Week 3

4.3 Electric Motors and Generators

Distinguish between an electric motor and a generator.

An ELECTRIC MOTOR converts electrical energy into mechanical (kinetic) energy. A GENERATOR converts mechanical energy into electrical energy. Both devices use the relationship between electricity and magnetism — but they operate as the REVERSE of each other.

Formula

Force on a current-carrying conductor in a magnetic field

F=BILsin⁡θF = BIL\sin\theta

F = force (N), B = magnetic field strength (T), I = current (A), L = length of conductor in the field (m), θ = angle between conductor and field

SI unit: N (newton)

THE ELECTRIC MOTOR: When a current-carrying loop is placed in a magnetic field, the force F = BIL acts on the loop (the motor effect). The two sides of the loop experience forces in opposite directions (by the right-hand rule), creating a turning effect (torque). This torque rotates the loop — converting electrical energy to mechanical energy. A split-ring commutator keeps the current flowing in the correct direction so that the torque always acts in the same rotational direction.

THE GENERATOR: When a loop of wire is rotated mechanically inside a magnetic field, the flux through the loop changes continuously. By Faraday's law, this changing flux induces an emf (and hence a current) in the loop. Mechanical energy (the rotation) is converted to electrical energy. An AC generator uses slip rings; a DC generator uses a split-ring commutator.

MOTORElectrical → MechanicalInput: current (I)Output: rotationvsGEN.Mechanical → ElectricalInput: rotationOutput: emf
Figure 4.4 — Left: Electric motor. Current is supplied to the coil; force on current in the magnetic field causes rotation (electrical → mechanical). Right: Generator. Mechanical rotation is applied; changing flux induces an emf (mechanical → electrical). Note how the two devices are structural mirrors of each other.

Electric Motor vs Generator

PropertyElectric MotorGenerator
Energy conversionElectrical energy → Mechanical energyMechanical energy → Electrical energy
InputCurrent (supplied from power source)Mechanical rotation (turbine, engine)
OutputRotation / movementInduced emf / current
Key principle usedForce on current in a field: F = BIL sinθFaraday's law: E = −N(Δφ/Δt)
Current direction deviceSplit-ring commutator (DC motor) or AC supply (AC motor)Slip rings (AC generator) or commutator (DC generator)
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Real World

REAL-WORLD APPLICATION: The electric motor in a hair dryer uses F = BIL to spin a fan. The generator at a power station uses Faraday's law as steam turbines rotate large coils in magnetic fields, producing the AC electricity supplied to homes.

Worked Example

A conductor of length 0,15 m carries a current of 4 A. It is placed in a uniform magnetic field of 0,3 T. The angle between the conductor and the field is 90°. Calculate the force on the conductor.

Given

  • L = 0,15 m
  • I = 4 A
  • B = 0,3 T
  • θ = 90°

Find

F = ?

Solution

  1. 1F = BIL sinθ
  2. 2F = (0,3)(4)(0,15) sin90°
  3. 3F = (0,3)(4)(0,15)(1)
  4. 4F = 0,18 N
Answer: F = 0,18 N
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Practice Question

State TWO differences between an electric motor and an electric generator. For each device, name the energy conversion that takes place.

(6 marks)

Next

Electric Circuits

Electromagnetism Grade 11 Physical Sciences CAPS Notes | MathSciBuddy