Magnetic Fields

Overview

Magnetic fields describe how magnets and electric currents influence the space around them. They are fundamental to motors, generators, transformers, loudspeakers, magnetic storage devices, and many modern technologies.

For H2 Physics, this chapter focuses on:

• what a magnetic field is
• how magnetic fields are represented
• magnetic flux density $B$
• magnetic fields produced by electric currents
• simple field calculations
• comparing field patterns

This topic is closely linked to:

• Current Electricity Fundamentals
• Magnetic Force
• Electromagnetic Induction

Core Ideas

Magnetic-fields questions revolve around a few main ideas:

• moving charges and electric currents produce magnetic fields
• magnetic fields are represented by field lines and magnetic flux density $\vec{B}$
• current geometry determines field pattern
• the right-hand grip rule sets field direction from conventional current
• magnetic fields from multiple sources combine by vector addition
• solenoids and electromagnets are practical ways to create stronger, more controlled fields

Exam Relevance

Students are expected to:

• interpret field diagrams and direction conventions correctly
• distinguish straight-wire, coil, and solenoid field patterns
• apply the right-hand grip rule using conventional current
• use standard proportional reasoning or simple formulas for current-produced fields
• explain why solenoids and electromagnets behave the way they do

Core Physical Idea

A moving electric charge produces a magnetic field.

This means electric current, which is moving charge, can create magnetic effects. Different conductor shapes create different magnetic field patterns.

Magnetic fields can also exert forces on moving charges and currents, studied later in Magnetic Force.

Key Representations

What Is a Magnetic Field?

A magnetic field is a region where:

• a magnetic material may experience a force
• a moving charged particle may experience a force
• a current-carrying conductor may experience a force

The field is represented by magnetic flux density:

$$\vec{B}$$

Its magnitude is:

$$B$$

SI unit:

$$\text{tesla (T)}$$

Magnetic Field Lines

Magnetic field lines are diagrams used to represent magnetic fields.

Rules

• outside a magnet, field lines go from North pole to South pole
• field lines form continuous loops
• the tangent to a field line gives field direction
• field lines never cross
• closer spacing means stronger field

Figure: Magnetic field lines around a bar magnet. Outside the magnet, field lines go from North to South.

Symbols in 2D Diagrams

• $\times$ : field into page
• $\bullet$ : field out of page

Figure: Dot-and-cross notation for magnetic field direction in 2D diagrams.

Uniform vs Non-Uniform Fields

Uniform Magnetic Field

A uniform field has:

• parallel lines
• equal spacing
• constant direction
• constant magnitude

Figure: Uniform magnetic field represented by parallel, equally spaced field lines.

Example:

• central region inside a long solenoid

Non-Uniform Magnetic Field

A non-uniform field has changing spacing and/or changing direction.

Example:

• field near a bar magnet
• field near a straight wire

Magnetic Flux Density

Magnetic flux density measures magnetic field strength.

Larger $B$ means stronger magnetic effects.

It is a vector quantity, so direction matters.

Where only size is needed, use scalar $B$.

Fields Produced by Currents Overview

Electric current produces magnetic fields.

Detailed treatment: Magnetic Fields from Currents

Long Straight Wire

Field lines are concentric circles around the wire.

Magnitude:

$$B=\frac{{\mu }_{0}I}{2\pi r}$$

where:

• $I$ = current
• $r$ = perpendicular distance from wire
• ${\mu }_0$ = permeability of free space

Field strength decreases as distance increases.

Circular Coil

A current-carrying circular coil produces a concentrated field near its centre.

At the centre:

$$B=\frac{{\mu }_{0}NI}{2r}$$

where:

• $N$ = number of turns
• $r$ = radius

Solenoid

A solenoid is a long coil of wire.

Inside the central region:

• field is strong
• field is approximately uniform

For a long solenoid:

$$B={\mu }_{0}nI$$

where:

• $n$ = turns per unit length

More details: Solenoids and Electromagnets

Right-Hand Grip Rule Overview

Used to determine field direction around a current.

Straight Wire

• thumb points in direction of current
• curled fingers show magnetic field direction

Solenoid or Coil

• fingers follow current around the turns
• thumb points to the solenoid North pole and internal field direction

Detailed page: Magnetic Fields from Currents

Electromagnet Overview

A solenoid with a soft iron core forms an electromagnet.

Advantages:

• can be switched on or off
• strength can be varied
• polarity can be reversed by reversing current

Detailed page: Solenoids and Electromagnets

Earth’s Magnetic Field

Earth behaves approximately like a large magnet.

Useful effects:

• a compass aligns with Earth’s field
• it helps navigation

Typical field strength:

$$\sim 50\mu \text{T}$$

Earth’s field is weak compared with laboratory electromagnets.

Superposition of Magnetic Fields

If several sources create magnetic fields at the same point, the resultant field is the vector sum.

Use ideas from Vectors.

Examples:

• two nearby wires
• coil plus external magnet
• multiple conductors

Comparing Field Patterns

Straight Wire

• circular field lines
• strongest near wire

Circular Coil

• stronger concentrated central region
• resembles short bar magnet

Long Solenoid

• nearly uniform field inside
• weak field outside

Bar Magnet

• non-uniform external field from North to South

Short Worked Examples

Example 1: Straight Wire Trend

A point is moved further from a wire carrying constant current.

Since:

$$B=\frac{{\mu }_{0}I}{2\pi r}$$

as $r$ increases, $B$ decreases.

Example 2: Stronger Solenoid

Two identical solenoids, but one carries double current.

Since:

$$B={\mu }_{0}nI$$

doubling $I$ doubles $B$.

Example 3: Coil with More Turns

If $N$ increases, the field at the centre increases proportionally.

Common Exam Traps Overview

Detailed page: Magnetic Fields Common Exam Traps

Frequent mistakes:

• using the wrong right-hand grip direction
• drawing crossing field lines
• confusing field with force
• assuming outside a solenoid field is exactly zero
• forgetting magnetic fields add vectorially
• misidentifying the North pole of a solenoid

Summary Sheet

Definitions

• magnetic field: region where magnetic effects act
• magnetic flux density: $\vec{B}$

Key Formulae

Straight Wire

$$B=\frac{{\mu }_{0}I}{2\pi r}$$

Circular Coil Centre

$$B=\frac{{\mu }_{0}NI}{2r}$$

Long Solenoid

$$B={\mu }_{0}nI$$

Direction Rules

• straight wire: right-hand grip rule
• solenoid: thumb gives North pole

Field Strength Factors

Increase by:

• larger current
• more turns
• smaller coil radius at coil centre
• soft iron core for an electromagnet

Links

• Magnetic Fields from Currents
• Solenoids and Electromagnets
• Magnetic Fields Common Exam Traps
• Current Electricity Fundamentals
• Magnetic Force
• Electromagnetic Induction
• Vectors