20.4 Magnetic Fields Due to Currents


2026 Syllabus Objectives

By the end of these notes, you should be able to:

  1. Sketch magnetic field patterns produced by the current in a long straight wire, a flat circular coil, and a long solenoid.
  2. Understand that the magnetic field of a solenoid is made stronger by placing a ferrous (iron-rich) core inside it.
  3. Explain why forces exist between two current-carrying conductors, and determine the direction of those forces.

1. How Does Current Create a Magnetic Field?

Whenever an electric current flows through a wire, it creates a magnetic field (an invisible region of force) in the space around it. This is one of the most important ideas in electromagnetism — electricity and magnetism are connected.

The shape and direction of the magnetic field depend on the shape of the wire and the direction of the current flowing through it.

There are three important shapes you need to know:

  • A long straight wire
  • A flat circular coil
  • A long solenoid (a coil of many loops)

2. The Right-Hand Grip Rule

Before looking at each shape, you need to know one key tool: the Right-Hand Grip Rule. This rule tells you the direction of the magnetic field around a current-carrying wire.

How to use it:

Imagine gripping the wire with your right hand. Point your thumb in the direction of the current (conventional current — from positive to negative). Your curled fingers show the direction the magnetic field lines circle around the wire.

Important notation:

  • A current coming out of the page towards you is shown as a dot (•) inside a circle.
  • A current going into the page away from you is shown as a cross (✕) inside a circle.
Current DirectionField Direction (viewed from above or front)
Upwards (out of page — dot)Anti-clockwise
Downwards (into page — cross)Clockwise

Think of it this way: the dot is the tip of an arrow flying towards you; the cross is the tail feathers of an arrow flying away from you.


3. Magnetic Field Pattern: Long Straight Wire

When current flows through a long, straight wire, the magnetic field lines form concentric circles — perfect rings centred on the wire.

Key features to draw and remember:

  • The field lines are circles centred on the wire.
  • The circles are closer together near the wire — this shows the field is strongest close to the wire.
  • The circles get further apart as you move away — the field gets weaker with distance.
  • Every field line must have an arrow showing its direction (clockwise or anti-clockwise, depending on current direction).
  • Reversing the current reverses the direction of the field.

How to sketch it:

Draw a dot or cross in the centre (representing the wire in cross-section). Then draw at least four concentric circles around it, with the inner circles closer together and the outer circles more spread out. Add arrows in the correct rotational direction.

📝 Exam Tip: Always draw arrows on every field line. Examiners will deduct marks if arrows are missing. Also make sure the spacing between circles increases as you go outward — this shows the field weakening with distance.

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