Magnetic field around a straight wire

In 1820, Hans Christian Ørsted noticed that a compass needle swung round whenever he switched on a current in a nearby wire. It was the first evidence that electricity and magnetism are linked: an electric current produces a magnetic field. This lesson describes the field around a straight wire, how to find its direction, and how it changes with the current.

The field pattern

The field lines around a long straight wire are concentric circles centred on the wire, in planes at right angles to it.

The circular pattern has the symmetry of a long straight wire: the field has the same strength all the way round at a given distance. The right-hand grip rule below sets the direction around each circle.

• The field is strongest close to the wire, so the circles are drawn closer together there and further apart further out.
• Viewed end-on, a dot (⊙) shows current coming out of the page, like the tip of an arrow coming towards you. A cross (⊗) shows current going into the page, like the tail feathers of an arrow moving away.

The right-hand grip rule

To find the direction of the field, grip the wire with your right hand:

1. point your thumb in the direction of the conventional current;
2. your fingers curl in the direction of the magnetic field.

Use conventional current, from positive to negative, not the electron flow. The rule was set up for conventional current; the electrons move the opposite way.

Worked example 1

Current out of the page

Problem

An end-on diagram shows conventional current coming out of the page, ⊙. State the direction of the magnetic field around the wire.

Show full solution

1. Point the thumb

   Method

   Point your right thumb out of the page, towards you.

   Reason

   The thumb shows the direction of conventional current.

   Working

   Answer

   Current: ⊙, out of the page.

2. Read the fingers

   Method

   Look at the way your fingers curl as you look down at the page.

   Reason

   The curl of the fingers is the direction of the field lines.

   Working

   Answer

   The field lines are anticlockwise circles.

Quick check

Set the thumb first and then read the fingers each time, rather than trying to remember which way the circles go.

Try it yourself 1

Finding the current from the field

Minimal support

Problem

Viewed end-on, the field lines around a wire are clockwise. Is the conventional current into or out of the page?

Use the rule backwards

Conventional current

Out of the page (dot).CorrectIncorrectInto the page (cross).CorrectIncorrect

Reason

Thumb follows the field; fingers show conventional current.CorrectIncorrectFingers follow the field; thumb shows electron drift.CorrectIncorrectFingers follow the field; thumb shows conventional current.CorrectIncorrect

Check answer

Hints

Hint 1

use the rule backwards

Curl the fingers of your right hand clockwise.

Hint 2

thumb

Which way does your thumb point now?

Show solution step by step

1. Set the fingers

   Method

   Curl your right-hand fingers clockwise, as seen looking at the page.

   Reason

   The fingers stand for the field, which is the direction you know.

   Working

   Answer

   Field: clockwise.

2. Read the thumb

   Method

   Your thumb points into the page, away from you.

   Reason

   The thumb gives the direction of the conventional current.

   Working

   Answer

   The current is into the page, ⊗.

Quick check

The grip rule works in both directions: from current to field, or from field back to current.

Check your understanding 1 Choose current and tangent

Electrons drift into the page through a long straight wire. Before drawing, find the conventional-current direction and the field direction directly to the right of the wire. Ignore the Earth’s field.

Conventional current

Out of the page (dot).CorrectIncorrectInto the page (cross).CorrectIncorrect

Field directly to the right

Towards the top of the page.CorrectIncorrectTowards the bottom of the page.CorrectIncorrectDirectly away from the wire.CorrectIncorrect

Check answer

Show answer

Conventional current is out of the page. With your right thumb towards you, the fingers curl anticlockwise. At the right-hand side of an anticlockwise circle, the tangent points upwards. A compass’s north end follows that local direction.

Check your understanding 2

Electrons drift into the page through a long straight wire. Draw an end-on field pattern and mark the conventional-current direction. A small compass is placed directly to the right of the wire, where the wire’s field dominates the Earth’s field. Which way does the compass’s north end point?

Draw the pattern on paper, then compare it with the figure and criteria. Add a note here only if useful; you need not type a description of every line.

Optional note from your sketch or comparison

Show answer

Conventional current is opposite to electron flow, so it is out of the page, marked with a dot (⊙). Draw concentric circles centred on the wire, spreading further apart outwards, with anticlockwise arrows. Directly to the right of the wire, the field is towards the top of the page, so the compass’s north end points upwards. The reference figure shows both conventional-current directions:

Check your understanding 3

A compass sits just below a straight wire. When a current is switched on, the needle turns away from north; when the current is switched off, it swings back. Explain both observations.

Field turning the compass with current on

Earth’s field alone, with current on.CorrectIncorrectWire’s field alone, with current on.CorrectIncorrectCombined fields of wire and Earth.CorrectIncorrect

After switching off

Neither field remains; the needle loses magnetism.CorrectIncorrectEarth’s field remains; wire’s field disappears.CorrectIncorrectBoth fields remain; the wire retains its field.CorrectIncorrect

Check answer

Show answer

When the current flows, it produces a magnetic field around the wire. The compass aligns with the combined field of the wire and the Earth, so it turns away from its original direction in this setup. The wire’s field can deflect the needle even when it is weaker than the Earth’s field. When the current stops, the wire’s field disappears, and the Earth’s field turns the still-magnetised needle back towards north.

Changing the current

• Increasing the current makes the field stronger at every point. The pattern stays the same, but the circles are drawn closer together.
• Reversing the current reverses the direction of the field, so every arrow turns round. At a given point, the strength is unchanged if the size of the current is unchanged.
• Moving further from the wire makes the field weaker.

You can reverse the current and watch the compasses respond in the magnetism and induction lab.

Spot the mistake 1

Reversing the current

About 5 min

Learner response

The current in a wire is reversed, keeping its size the same. A learner says the field at a nearby point becomes weaker but keeps its direction. Correct both parts of the claim.

Check both corrections

Field direction at the same nearby point

Reverses.CorrectIncorrectStays the same.CorrectIncorrect

Field strength at that point

Stays the same at unchanged current magnitude.CorrectIncorrectGets stronger at unchanged current magnitude.CorrectIncorrectGets weaker at unchanged current magnitude.CorrectIncorrect

Check answer

Show solution step by step

1. Direction

   Method

   The field reverses: clockwise becomes anticlockwise, or the other way round.

   Reason

   Reversing the thumb in the grip rule reverses the curl of the fingers.

   Working

   Answer

   Current reversed, so field reversed.

2. Strength

   Method

   The strength at the point stays the same.

   Reason

   The strength depends on the size of the current and the distance from the wire, and neither has changed.

   Working

   Answer

   Same current size, same distance, so same field strength.

Common mistake

The direction of the current sets the direction of the field; the size of the current sets its strength.

Check your understanding 4 Change size and direction together

The current through a long wire doubles in magnitude and reverses direction. A compass is kept at the same point, with the wire’s field dominating the Earth’s field. Explain what changes in the field’s shape, strength and direction, and what the compass does. Work on paper or here, then compare all parts below; the note is optional.

Optional note from your reasoning or comparison

Show answer

The field lines remain concentric circles centred on the wire. The field at the same point is stronger because the current magnitude has increased, and its direction reverses because the current direction has reversed. The compass’s north end turns to follow the reversed local field. Check shape, strength, direction and compass alignment separately; a stronger field does not mean a different circular shape or a radial arrow.

Common mistakes

• Using the direction of electron flow with the grip rule. Use conventional current.
• Drawing straight field lines coming out of the wire. They are circles around it.
• Drawing the circles evenly spaced. They spread out further from the wire, where the field is weaker.
• Mixing up the symbols: a dot is current coming out of the page, a cross is current going into it.
• Saying that reversing the current at unchanged magnitude changes the field strength. At the same point, it changes only the direction.