Year 11 Physics Module 4 ⏱ ~35 min 5 MC · 3 Short Answer Lesson 12 of 17

Magnetic Fields & Field Lines

Royal North Shore Hospital's 3 T MRI scanner (installed 2019): the core is a niobium-titanium (NbTi) solenoid cooled to 4 K by liquid helium. At 3 Tesla, 60,000 times Earth's magnetic field, proton nuclei precess in alignment and can be detected to produce detailed tissue images. Magnetic field lines, invisible to the naked eye, reveal everything about the geometry of such fields.

Today's hook: Royal North Shore Hospital's 3 T MRI scanner (installed 2019) uses a superconducting solenoid cooled to 4 K to produce a field of 3 Tesla, 60,000 times Earth's field of 50 μT. The field lines inside that solenoid run straight, parallel, and equally spaced: a textbook uniform field. Outside, lines flare out and return to the ends. What rules govern how all magnetic field lines behave?
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Warm up first

Warm up first

Three quick questions from earlier lessons. Pulling old material back to mind before you learn something new makes the new material stick better, so this is not busywork.

Before you read, predict

A bar magnet is placed on a table. Iron filings are scattered around it.

Predict 1: Where will the iron filings be most densely packed, and why?

Predict 2: What direction will a compass point if placed halfway along the side of the magnet?

Magnetic field lines are drawn to exit from which pole of a bar magnet?

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Learning Intentions

Learning Intentions

Know

  • Field lines exit the north pole and enter the south pole of a magnet
  • Field line density represents field strength (B)
  • Field lines never cross
  • Sources: permanent magnets, current-carrying conductors, solenoids

Understand

  • Why field lines are a model, not a physical reality
  • Strengths of the model: direction, relative strength, field geometry
  • Limitations: cannot show field magnitude quantitatively; lines are 2D representations of a 3D field

Can Do

  • Draw field lines for a bar magnet, between two poles, and along a straight wire
  • Use field line density to compare field strengths
  • Identify strengths and limitations of the field line model
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Key Terms

Key Terms
Magnetic field ($\boldsymbol{B}$)A region of space where a magnetic force can be detected. A vector quantity; SI unit: Tesla (T).
Magnetic field lineA line drawn so that its tangent at any point gives the direction of $\boldsymbol{B}$ at that point. Density of lines indicates relative field strength.
North poleThe pole from which field lines conventionally emerge. A free north pole would be repelled by the north pole of another magnet.
Uniform fieldA field with equal magnitude and direction everywhere in a region. Represented by parallel, equally-spaced field lines (e.g. between flat pole faces).
Cross-lesson links: L12 opens the magnetism section of M4. Electric fields (L01–L04) were produced by static charges; magnetic fields are produced by moving charges, this connection deepens in L13 (current-carrying wires) and L14 (solenoids). The Royal North Shore 3 T MRI solenoid produces a field 60,000× Earth's, visualised entirely using the field line model introduced here.
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Rules for Magnetic Field Lines

Core Content

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Rules for Magnetic Field Lines
+5 XP

Hold a bar magnet under a sheet of white paper and sprinkle iron filings on top. Tap the paper gently, the filings snap into curving arcs that run from one end of the magnet to the other, bunched densely at the tips and spreading out broadly in the middle. No one drew those lines; the filings are simply aligning with an invisible force field that already exists in the space around the magnet. Magnetic field lines are our way of drawing that pattern, they are a map of a region of space that exerts a force on magnets and moving charges.

Five rules for field lines
  1. Lines exit from north poles and enter south poles (outside the magnet).
  2. Lines form continuous closed loops (including through the magnet).
  3. Lines never cross, each point in space has only one field direction.
  4. Lines are closer together where the field is stronger.
  5. Lines point in the direction a free north pole would move.
Comparison of closed magnetic field loops around a bar magnet, diverging non-crossing lines and a neutral point between facing north poles, and dense nearly parallel lines from north to south between unlike poles.
Outside a magnet, arrows run from N to S; inside, they return from S to N to complete each loop. Like poles make the lines diverge, while unlike poles concentrate them across the gap.

Trace: Follow one complete loop in panel 1, then compare the line direction and spacing in the central gaps of panels 2 and 3.

Strengths and limitations of the model

Model evaluation

Strengths: shows direction of $\boldsymbol{B}$; shows relative field strength (density); shows field geometry (uniform vs. diverging); predicts behaviour of compass needles.

Limitations: lines are a 2D representation of a 3D field; density of lines cannot give absolute values of $B$; suggests the field exists only along the lines (misleading, field exists everywhere); model does not explain the underlying physics (moving charges).

Magnetic field lines exit north poles and enter south poles, form continuous closed loops, never cross, and are denser where the field is stronger. The model shows direction and relative strength but cannot give absolute values of $B$ and falsely implies the field exists only along drawn lines.

Pause, write the highlighted rules and model limits into your book.

Magnetic field lines can cross each other at right angles.

Closely packed magnetic field lines indicate a stronger magnetic field.

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Activity 1, Describing Magnetic Field Patterns

Activity 1, Describing Magnetic Field Patterns
UnderstandBand 2

For each configuration, describe the magnetic field pattern (direction of lines, where lines are most dense, and whether the field is uniform):

  1. A bar magnet in isolation
  2. Two north poles facing each other
  3. A north pole facing a south pole

Between two opposite magnetic poles (north facing south), the field lines are:

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Activity 2, Model Strengths and Limitations

Activity 2, Model Strengths and Limitations
EvaluateBand 5

A physics student uses a field line diagram showing 10 lines around a bar magnet to conclude: "There are exactly 10 field lines around this magnet, and no field exists between them."

  1. Identify two errors in the student's reasoning.
  2. State one genuine strength of the field line model.
  3. Explain what a field line diagram can and cannot tell you about the magnitude of $B$.

Three of these are correct rules for magnetic field lines. Pick the odd one out.

Magnetic field lines form _____ closed loops, meaning they have no start or end point.

A major limitation of the magnetic field line model is that:

✓

Show what you have learned

Quick recall, magnetic field lines
+5 XP
Short Answer, 10 marks
+5 XP

UnderstandBand 2(3 marks) 3. State three rules that govern the drawing of magnetic field lines. For each rule, give a reason based on the physical behaviour of the field.

AnalyseBand 4(3 marks) 4. Two identical bar magnets are placed with their north poles 10 cm apart. (a) Describe the field pattern between the poles. (b) Identify where a neutral point would form. (c) Explain what "neutral point" means in terms of the magnetic field.

EvaluateBand 6(4 marks) 5. Evaluate the magnetic field line model as a scientific model. In your response, discuss what the model predicts correctly, what it fails to describe, and how the model relates to the underlying physical reality of magnetic fields being produced by moving charges.

Show all answers

Activity 1, Model Answers

  1. Bar magnet: Lines exit from north pole, curve around, and enter south pole. Most dense near the poles (strongest field). Non-uniform, diverge away from poles.
  2. Two N poles: Lines from each N pole curve away and repel each other. A neutral point forms midway where lines from each magnet cancel. Field is zero at the neutral point.
  3. N facing S (attracting): Lines go from N to S. Between the poles, lines are nearly parallel and equally spaced → uniform field. Most dense immediately at the poles. Field is stronger near the poles.

Activity 2, Model Answers

  1. Error 1: The field line model uses an arbitrary number of lines, there are infinitely many field lines; 10 is a representation choice, not a physical fact. Error 2: The field exists everywhere in space, not just along the drawn lines, the absence of a drawn line does not mean the field is zero.
  2. Strength: The model correctly shows the direction of the field at any point (tangent to the line) and shows where the field is relatively stronger (denser lines).
  3. Can tell: relative direction of $\boldsymbol{B}$ and comparative strength (where lines are denser, $B$ is larger). Cannot tell: absolute magnitude of $B$ in tesla, the number of lines chosen is arbitrary.

Short Answer, Model Answers

Q3 (3 marks): (1) Lines exit north poles and enter south poles externally, because a free north pole would be repelled from north and attracted to south, the line direction shows this motion. (2) Lines never cross, at any single point in space, the magnetic field has only one direction; two crossing lines would imply two directions at one point, which is impossible. (3) Lines are closer together where the field is stronger, this represents the field density ($B$), analogous to how many lines pass through a unit area perpendicular to the field.

Q4 (3 marks): (a) Between two N poles, field lines from each magnet curve away from each other, creating an opposing pattern. Lines do not connect the two poles directly, they are repelled. (b) A neutral point forms at the midpoint between the two poles (by symmetry), where the contributions from each magnet are equal and opposite. (c) A neutral point is a location where the net magnetic field is zero, the contributions from the two sources cancel exactly. A compass at a neutral point experiences no net force.

Q5 (4 marks): The field line model correctly predicts: direction of force on a magnetic dipole at any location; relative field strength (denser lines = stronger field); the shape of fields around common sources (bar magnets, solenoids). It fails to describe: the absolute magnitude of $B$ (the number of lines is arbitrary); the 3D nature of the field (diagrams are 2D cross-sections); the underlying physical mechanism, magnetic fields are produced by moving charges (electrons in orbit and spin). The model also incorrectly implies the field only exists where lines are drawn. The underlying reality is that $\boldsymbol{B}$ is a vector field defined at every point in space; its source is the motion of electric charges. Field lines are a useful geometric abstraction of this continuous vector field, not a physical entity.

✓

Retrieve, reflect and finish

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How did your thinking change?

Royal North Shore Hospital's 3 T MRI scanner (2019) is a superconducting solenoid cooled to 4 K. Its field of 3 Tesla, 60,000× Earth's 50 μT, is a nearly perfect uniform field inside the bore: parallel, equally spaced field lines running the length of the solenoid. Outside, lines flare from the ends and loop back, exactly the pattern you would see if you could scatter iron filings around a very long, very powerful bar magnet. Every rule for field lines applies directly to that MRI scanner.

Now check your Think First answers: iron filings are most dense near the poles, where field lines are closest together and B is greatest. A compass halfway along the side aligns tangentially to the field lines, pointing roughly parallel to the magnet's long axis, toward the nearer pole.

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