Magnetic Fields from Currents
Overview
A key idea in electromagnetism is that electric current produces magnetic fields. Since current is moving charge, any conductor carrying current creates a magnetic field around it.
The shape and strength of the field depend on:
- conductor geometry
- current
- distance from conductor
- number of turns for coils
- presence of magnetic core for solenoids
This page deepens the current-produced fields introduced in Magnetic Fields.
Definition
A current-produced magnetic field is the magnetic field generated by moving charges in a conductor.
Different current paths produce different field patterns.
Why It Matters
This is the foundation for:
- electromagnets
- motors
- relays
- transformers
- later magnetic-force and electromagnetic-induction topics
Core Physical Idea
Charges in motion generate magnetic fields.
Hence:
- straight wire current gives a circular field
- circular coil current gives a concentrated central field
- many loops combined give a strong solenoid field
Key Representations
Right-Hand Grip Rule
This rule determines magnetic field direction around conventional current.
Straight Wire
- thumb points in direction of current
- curled fingers show direction of magnetic field lines
Coil or Solenoid
- fingers curl in direction of current around the coil
- thumb points to:
- internal magnetic field direction
- North pole of the solenoid
Magnetic Field Around a Long Straight Wire
Field Pattern
The field lines are concentric circles centred on the wire.
- strongest near the wire
- weaker further away
The field is non-uniform.
Figure: Magnetic field around a straight current-carrying wire.
Magnitude
where:
- = current
- = perpendicular distance from wire
- = permeability of free space
Trends
If current doubles, doubles.
If distance doubles, halves.
Notes
Distance must be measured perpendicularly from the wire.
Straight Wire Examples
Current Upward
Viewed from above:
- field circles anticlockwise
Current Downward
- field circles clockwise
Figure: Three-dimensional view of the magnetic field around a straight current-carrying wire.
Magnetic Field Around a Circular Coil
Field Pattern
Each part of the wire contributes magnetic field at the centre.
These combine to produce a stronger resultant field through the centre.
The pattern resembles a short bar magnet.
Figure: Magnetic field pattern around a circular current-carrying wire, showing a concentrated field through the centre.
Magnitude at Centre
where:
- = number of turns
- = current
- = radius
Trends
Increase by:
- increasing current
- increasing number of turns
- decreasing radius
Why Coils Strengthen Fields
A single wire loop creates field contributions that reinforce one another at the centre.
More turns means more reinforcing contributions.
Hence coils are much more useful than single wires for producing strong fields.
Magnetic Field of a Solenoid
A solenoid is a long helical coil carrying current.
Detailed applications: Solenoids and Electromagnets
Field Pattern
Inside Solenoid
- nearly parallel field lines
- nearly equal spacing
- approximately uniform field
Outside Solenoid
- weak returning field lines
- resembles bar magnet external field
Figure: Magnetic field pattern of a solenoid, with a strong nearly uniform field inside and weaker returning field lines outside.
Magnitude for a Long Solenoid
where:
- = turns per unit length
- = current
Solenoid Trends
Increase field strength by:
- increasing current
- increasing turns per unit length
- using a soft iron core
Why Solenoid Field Is Strong
Each loop contributes field in the same internal direction.
These contributions add strongly inside the solenoid.
Outside, many contributions partially cancel.
Comparing Field Patterns
Straight Wire
- concentric circles
- non-uniform
- strongest near wire
Circular Coil
- concentrated centre field
- bar-magnet-like pattern
Long Solenoid
- strong uniform internal field
- weak external field
Relative Field Strength Logic
Use line spacing qualitatively.
Closer lines indicate stronger field.
Examples
Straight Wire
Closer to the wire means stronger field.
Solenoid
The inside centre region is stronger than the outside.
Coil
The centre is stronger than a distant external region.
Multiple Current-Carrying Conductors
If two or more conductors produce fields at one point:
- fields combine by vector addition
Use Vectors.
This becomes important in later force topics.
Short Worked Examples
Example 1
A wire current is doubled while distance remains constant.
Since:
the field doubles.
Example 2
A point moves from distance to from a wire.
Since:
the field halves.
Example 3
Two identical coils, but one has twice the number of turns.
The second coil has twice the field at the centre.
Common Mistakes
- Using the wrong hand rule
- Using the wrong distance from a wire
- Assuming the outside solenoid field is zero
- Mixing coil and solenoid formulae
- Ignoring number of turns
Summary
Straight Wire
Circular field lines.
Circular Coil
Strong centre field.
Long Solenoid
Strong approximately uniform internal field.
General Rule
More current and more aligned turns give stronger magnetic fields.