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F3.5 · Diagram the production and interaction of magnetic fields

Learn to diagram the production and interaction of magnetic fields through clear examples and targeted practice.

Ontario Grade 11 Physics

Electricity and Magnetism

SPH3U study topic F3.5

A magnetic field is the region around a magnet or an electric current where magnetic effects can be detected. A field has both strength and direction, so it is a vector. A vector diagram uses arrows to show direction; longer or denser arrows can represent a stronger field. A scalar has magnitude only, such as a temperature. In this lesson, diagrams are models: they show field patterns, not visible lines in space. We will first review how to read arrows, then diagram field production and interaction.

What you will learn

1. Prerequisite bridge: reading field diagrams

A direction needs a reference. For the diagrams in this lesson, north is up, east is right, south is down, and west is left. The direction of a field at a point is the direction a small north pole would be pushed. This is a way to define the arrow direction; the field itself is not a stream of particles.
Magnetic field lines are drawn as smooth curves with arrows. They are closer together where the field is stronger and farther apart where it is weaker. The lines do not cross: if they crossed, the field at that point would have two directions.
Outside a bar magnet, field-line arrows point from the north pole toward the south pole. The full pattern forms closed loops: inside the magnet, the arrows return from south to north. Do not treat the lines as physical wires.

2. How magnets and electric currents produce fields

A permanent magnet produces a magnetic field around it. A bar magnet is a useful model because it has two poles, labelled north and south. To diagram its field, draw several curved lines leaving the north pole and entering the south pole outside the magnet. Add arrows to every line. Draw the lines closer together near the poles to show that the field is stronger there.
An electric current is moving electric charge in a conductor, such as a wire. A current-carrying wire also produces a magnetic field. Around a long, straight wire, the field lines form circles centred on the wire. The field direction is found with the right-hand grip rule. Point your right thumb in the direction of conventional current, which is the direction positive charge would move. Your curled fingers show the field direction around the wire.
For a wire drawn on a page, use a dot to show current coming out of the page toward you. Use a cross to show current going into the page away from you. These symbols represent the tip and tail of an arrow. With current coming out of the page, the circular field arrows go counterclockwise. Reversing the current reverses the field direction. A current direction must be shown before the field direction can be inferred.
Magnetic field strength is measured in teslas, symbol T\mathrm{T}. This lesson uses diagrams to compare directions and relative strength; it does not calculate field strength.
thumb: conventional current; curled fingers: magnetic field\text{thumb: conventional current; curled fingers: magnetic field}

3. How magnetic fields interact

When fields from two sources occupy the same region, the field at a point is the combined effect of both fields. This is called superposition: the fields combine direction by direction. In a diagram, show each source’s field and then draw the resulting pattern. Where the fields point in the same direction, the combined field is stronger. Where they point in opposite directions, they partly or fully cancel.
This idea explains familiar patterns between magnets. Opposite poles facing each other produce a field pattern that connects across the gap. The pattern is denser in the gap, so the field there is stronger. Like poles facing each other produce field lines that bend away from the space between the poles. The field pattern shows that the magnets repel; it does not mean that field lines physically push one another.
Field diagrams are qualitative models. They show the shape, direction, and relative strength of a field. They do not give a numerical field value unless measurements or a suitable calculation method are provided. For F3.5, the key task is to draw and interpret the patterns accurately.
B⃗result=B⃗1+B⃗2\vec{B}_{\mathrm{result}}=\vec{B}_1+\vec{B}_2

4. A reliable method for drawing

First identify the source or sources: a magnet, a current-carrying wire, or both. Mark the poles or state the conventional current direction. Next choose the reference directions on the page and mark whether any current points into or out of the page. Apply the right-hand grip rule when the source is a straight wire.
Draw smooth field lines with arrowheads. Check that each arrow follows the correct direction around its source. For magnets, include the return path inside the magnet if drawing complete loops. For multiple sources, show how the patterns combine in the region between them. Finally, check that closer spacing indicates stronger field and that no lines cross.
A quick consistency check is to reverse one source’s direction. If the current reverses, the wire’s field arrows must reverse too. If magnet poles are swapped, the outside field arrows must also reverse. This check helps catch diagrams that have correct shapes but incorrect directions.

Worked example

Field around a straight wire

A straight wire passes perpendicular to the page. Conventional current comes out of the page. Diagram the field direction around the wire.
  1. Set the reference
    Treat the wire as the source. The page is the diagram plane, and the current points toward the viewer. Mark the current with a dot. I out of page (\bullet)
  2. Apply the grip rule
    Point your right thumb toward yourself. Your fingers curl counterclockwise when viewed on the page, so the field arrows follow that direction.
    ↺\circlearrowleft
Answer: Draw concentric circles centred on the dot, with arrowheads counterclockwise. Label the dot as conventional current out of the page. Field direction is a vector direction; no field magnitude is specified.
Check: The diagram has circular lines around the wire and the direction agrees with the right-hand grip rule. No numerical value or unit conversion is needed because this is a direction-only diagram.

Worked example

Two poles facing across a gap

Two bar magnets are arranged with the north pole of the left magnet facing the south pole of the right magnet. Show the field pattern in the gap.
  1. Mark the poles
    The sources are two permanent magnets. Put N on the left-facing end of the left magnet and S on the left-facing end of the right magnet. Outside a magnet, field arrows point from north to south.
    N  ⟶  S\mathrm{N}\;\longrightarrow\;\mathrm{S}
  2. Draw the gap pattern
    Draw several field lines across the gap from the facing north pole to the facing south pole. Put arrows toward the south pole. Make the lines relatively close together in the gap to show a stronger field there.
    N  →  →  S\mathrm{N}\;\rightarrow\;\rightarrow\;\mathrm{S}
Answer: The gap contains connecting field lines directed from the left magnet’s north pole to the right magnet’s south pole. The pattern represents attraction between opposite poles.
Check: The arrows point from N to S outside the magnets. The denser gap pattern indicates relative strength, not a measured value, so no numerical field strength or tesla value can be reported.

Worked example

Like poles facing

Two magnets face one another with their north poles toward the gap. Describe a correct field diagram and the interaction it represents.
  1. Identify the sources
    Both facing ends are north poles. Outside each magnet, field arrows leave the north pole and head toward a south pole elsewhere in the complete pattern.
    N  N\mathrm{N}\;\qquad\mathrm{N}
  2. Show the combined pattern
    Draw the lines bending away from the region directly between the poles. Do not draw connecting arrows from one north pole into the other. The pattern between the poles indicates that the fields do not point in the same direction there.
    N  ↶↷  N\mathrm{N}\;\curvearrowleft\qquad\curvearrowright\;\mathrm{N}
Answer: The field lines curve away from the space between the facing north poles. This pattern represents repulsion between like poles.
Check: The diagram does not show field lines ending at a north pole, and the lines do not cross. It is a qualitative field pattern, so no force or field magnitude is calculated.

Common mistakes and how to avoid them

Drawing magnetic field arrows from south to north outside a bar magnet.
Correction: Outside the magnet, arrows go from north to south. They return inside the magnet to complete the loop.
Treating the dot and cross symbols as decorative marks.
Correction: A dot means current comes out of the page; a cross means it goes into the page. Use the right-hand grip rule from that direction.
Drawing field lines that cross or treating the lines as physical strings.
Correction: Lines are a model. They cannot cross because the field at one point has one direction.
Assuming every pair of nearby magnets has the same pattern.
Correction: Check which poles face. Opposite poles show lines connecting across the gap; like poles show lines bending away.

Lesson summary

Check your understanding

Question 1

A straight wire’s conventional current points into the page. Which way do its circular field arrows go when viewed on the page?
  1. Clockwise
  2. Counterclockwise
  3. Straight from left to right
  4. There is no field around the wire
Show answer and explanation
Clockwise
With the right thumb pointing into the page, the fingers curl clockwise.

Question 2

What do closer field lines in a diagram represent?
  1. A stronger field in that region
  2. A weaker field in that region
  3. A reversal of the field direction
  4. A location where the field lines cross
Show answer and explanation
A stronger field in that region
Closer spacing represents a stronger field. The arrows, not the spacing, show its direction.

Question 3

Two north poles face each other. Which pattern and interaction are appropriate?
  1. Lines connect directly from one north pole to the other; attraction
  2. Lines bend away from the gap; repulsion
  3. Lines stop at both north poles; no interaction
  4. Lines cross in the gap; attraction
Show answer and explanation
Lines bend away from the gap; repulsion
Like poles repel, and the field pattern bends away from the space between them.

Key terms

Magnetic field
The region around a magnet or electric current where magnetic effects can be detected.
Vector
A quantity with both magnitude and direction.
Conventional current
The direction positive charge would move in a circuit or conductor.
Field line
A drawn curve whose arrows show field direction and whose spacing compares field strength.
Superposition
The combining of fields in a region according to their directions.
Tesla
The SI unit used to measure magnetic field strength, symbol T\mathrm{T}.

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Published by DoAssignment. This AI-assisted lesson follows Ontario Grade 11 Physics (SPH3U), expectation F3.5. It is a study resource, not an official curriculum publication.

Before publication, the draft is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability, and then requires administrator approval. Errors can still occur, so corrections are welcomed.

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