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Magnetic Field Due To Current In A Straight Wire

Key idea: O Level electromagnetism: the magnetic field pattern around a straight current-carrying wire and how to use the right-hand grip rule.

  • SEC G3 Physics 2027
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Learning objectives

  • State the properties of magnets
  • Describe induced magnetism
  • Distinguish temporary and permanent magnets
  • Determine magnetic-field direction with a compass or bar magnet
  • Interpret bar-magnet field patterns
  • Draw the magnetic field pattern around a bar magnet and between the poles of two bar magnets
  • Interpret the field pattern around a straight current-carrying wire
  • Draw the magnetic field pattern around a straight current-carrying wire
  • Interpret the field pattern around a current-carrying solenoid
  • Draw the magnetic field pattern around a current-carrying solenoid
  • Relate current magnitude and direction to magnetic field
  • Describe electromagnet applications
  • Describe experiments showing the force on a current-carrying conductor in a magnetic field
  • Describe magnetic force on a charged-particle beam
  • Predict force reversal when current or field reverses
  • Use Fleming’s left-hand rule
  • Explain the turning effect on a current-carrying coil
  • Explain how current and turns increase the turning effect
  • Describe split-ring commutator action
  • Describe the effect of winding a motor coil on a soft-iron cylinder
  • Deduce that a changing magnetic field can induce an e.m.f.
  • Deduce that induced e.m.f. opposes the change producing it
  • Deduce factors affecting induced e.m.f. magnitude
  • Describe a simple a.c. generator and slip rings
  • Sketch a simple a.c. generator voltage–time graph
  • Describe a simple iron-cored transformer
  • Apply ideal-transformer equations
  • Explain cable loss and high-voltage transmission

1. Definition

A current in a straight wire produces a magnetic field with field lines that form concentric circles around the wire.

What you need for this course

You should be able to describe the magnetic field around a current-carrying straight wire and determine its direction.

2. Key Ideas

  • Pattern: magnetic field lines are circles centred on the wire.
  • Direction: use the right-hand grip rule (thumb = conventional current).
  • Bigger current → stronger magnetic field (qualitative).
  • Further from the wire → weaker magnetic field (qualitative).
  • Reverse the current → reverse the field direction.
  • On a page, ⊙ means current out of the page (arrow tip) and ⊗ means current into the page (arrow tail/feathers).

3. Detailed Explanations

A. Field pattern around a straight wire

Viewed end-on, the field lines are circles centred on the wire. A current out of the page (⊙) gives an anticlockwise field; a current into the page (⊗) gives a clockwise field.

B. Right-hand grip rule (direction)

  1. Point your right thumb in the direction of conventional current.
  2. Your fingers curl in the direction of the magnetic field.
Current-produced fields and the motor effectThree panels show an anticlockwise field around current out of the page; a longitudinal section through a solenoid, with current out of the page in the upper parts of every turn and into the page in the lower parts, giving internal field to the right and a north pole at the right end; and the motor-effect directions for field right, current out of the page and force up.Straight wireSolenoidMotor effectcurrent out of pagethumb points out; fingers curlanticlockwise around the wireLarger current → stronger field.Further away → weaker field.Section through the coil axisupper parts: I out of pageSNlower parts: I into pageinside field: S → NEach upper/lower pair belongsto the same coil turn.Curl fingers with current;thumb points right, to N.Return field outside not shown.B: N → SBIout of pageFupFleming’s left handfirst finger → field Bsecond finger → current Ithumb → force FReverse B or I → F reverses.Reverse both → F is unchanged.
Scroll diagram horizontally to read all labels.
Use the right-hand grip rule for fields made by currents; use Fleming’s left-hand rule for the force on a current in an external magnetic field.

C. Strength changes (qualitative)

Field lines are drawn closer together where the field is stronger. Near the wire, the field is stronger; further away, it is weaker.

Simulation checkpoint

In the Magnetism & Induction Lab, choose the straight-wire field. Read the fixed current direction, predict the circular field direction, then check the labelled probes. Increase the current and state what changes—and what does not change—about the pattern.

4. Common Mistakes

  • Using electron flow instead of conventional current for the right-hand rule.
  • Drawing straight field lines (they should be circles around the wire).
  • Forgetting that reversing current reverses the field direction.

5. Exam Tips

  1. If asked for the pattern: write “concentric circles around the wire”.
  2. If asked for direction: write “use the right-hand grip rule (thumb = current)”.
  3. If asked about reversing: “field direction reverses”.

6. Worked Examples

Modelled example 1

Field direction (qualitative)

Core

Problem

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

  1. Set the thumb

    Method

    Point the right thumb out of the page, toward you.

    Reason

    The thumb represents conventional current in the right-hand grip rule.

    Working

    Current: ⊙.

  2. Read the curled fingers

    Method

    State that the field is anticlockwise.

    Reason

    The curled right-hand fingers show the circular field direction.

    Working

    ⊙ I ⇒ B anticlockwise

Guided practice 2

Changing current

About 4 min

Problem

Points beside wires A and B are at the same distance from their wires. A carries the larger current. Which field is stronger at its point?

Hold distance fixed and vary one factor

Hints

Hint 1: controlled factor
Distance is the same for both.
Hint 2: current effect
A larger current produces a stronger field.
View solution step by step

  1. Compare the currents

    Method

    Choose wire A.

    Reason

    At equal distance, magnetic-field strength increases with current magnitude.

    Working

    I_A > I_B, r_A = r_B ⇒ B_A > B_B

Common misconception 3

Reversing the current

Find and correct the mistake

Learner response

At a fixed point, a wire’s current is reversed without changing its magnitude. A learner says the field becomes weaker but keeps the same direction. Diagnose both claims.

Separate current direction from magnitude

View solution step by step

  1. Reverse the field direction

    Method

    State that clockwise becomes anticlockwise or vice versa.

    Reason

    Reversing the thumb in the grip rule reverses the finger curl.

    Working

    I direction reverses ⇒ B direction reverses

  2. Keep the field strength

    Method

    State that the strength at the fixed point is unchanged.

    Reason

    Current magnitude and distance are unchanged.

    Working

    |I| and r fixed ⇒ |B| fixed

Examiner practice 4

Comparing distances

2 marks

Examination question

P is 1 cm and Q is 3 cm from the same current-carrying straight wire. Compare the magnetic-field strengths and explain. [2 marks]

Compare distance while current is fixed

View solution step by step

  1. Compare the fields

    2 marks

    Method

    State that the field is stronger at P.

    Reason

    The field around a straight wire weakens as distance from the wire increases.

    Working

    r_P < r_Q ⇒ B_P > B_Q

Challenge 5

Current direction from field direction

Minimal support

Inverse-rule transfer

Viewed end-on, the field around a wire is clockwise. Determine whether conventional current is into or out of the page.

Curl fingers with the known field first

Hints

Hint 1: reverse use
Curl your right-hand fingers clockwise.
Hint 2: thumb
Read the direction of your thumb.
View solution step by step

  1. Set the known curl

    Method

    Curl the right-hand fingers clockwise.

    Reason

    The fingers represent the observed field direction.

    Working

    B clockwise.

  2. Read the current

    Method

    State that current is into the page, ⊗.

    Reason

    The right thumb points away from you when the fingers curl clockwise.

    Working

    B clockwise ⇒ I:⊗

7. Mind Stretchers

Mind stretcher 1: Why circles?Extension

Why do the field lines form circles around a straight wire instead of going straight outwards?

Show Answer

The field direction around a straight wire wraps around the wire, so at each point the field is tangential to a circle centred on the wire. Field lines follow the field direction, so they form circles.

Mind stretcher 2: Compass near a wireExtension

A compass is placed near a straight wire. It deflects when current flows, and returns to its usual north–south direction when the current stops. Why?

Show Answer

When current flows, the wire produces a magnetic field that affects the compass direction. When the current stops, the wire’s magnetic field disappears, so the compass aligns mainly with Earth’s magnetic field again.

8. Practice and next step

Reverse the current in the Magnetism & Induction Lab, then continue to the Solenoid Field.

Continue with the next resource in this course.

Course and syllabus information
Course
SEC G3 Physics
Edition
SEC G3 Physics 2027