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D3.3 · Use diagrams to compare field sources and directions

Learn to use diagrams to compare field sources and directions through clear examples and targeted practice.

Ontario Grade 12 Physics

Gravitational, Electric, and Magnetic Fields

SPH4U study topic D3.3: reading and drawing field diagrams

A field describes how a source can influence objects or locations around it. A field diagram is a visual model. It uses lines and arrows to show field direction and sometimes relative strength. This lesson compares gravitational, electric, and magnetic fields. Before reading a diagram, identify its sources and viewpoint. A field direction is a vector direction; it does not state how fast an object moves.

What you will learn

Identify the source of gravitational, electric, and magnetic fields.
Use field-line diagrams to show and compare field directions.
Explain what arrows and spacing in a field diagram represent.
Avoid common errors when interpreting or drawing field diagrams.

1. Set up the system and read the diagram

A physical system is the set of objects being considered. For a field diagram, it may include a source, such as a charged sphere, and the surrounding region where its field is represented. The reference frame is the viewpoint used to describe positions and directions. For a stationary sketch, use a coordinate frame fixed to the page or source.

A positive direction is a chosen direction along an axis. For example, right might be positive on a horizontal axis. This choice helps assign signs to components, but it does not change the actual field. A scalar has magnitude only, such as mass. A vector has both magnitude and direction, such as a field at a point.

A field diagram represents field vectors at locations. An arrow points in the field’s direction at that location. It does not show an object’s velocity or the route the object must follow. When a question asks only for direction, a labelled arrow is often enough; a numerical calculation is not required.

Name the field source and identify the region shown.
Choose a reference frame and, when useful, label a positive direction.
Read each arrow as the field direction at its location.

2. Compare sources and direction rules

A gravitational field is associated with mass. Around an isolated mass, arrows point toward the mass. This is the direction a small test mass would be pulled. On either side of the source, the field points inward.

An electric field is associated with electric charge. Its direction is defined as the direction of the force on a small positive test charge. Around a positive source charge, arrows point outward. Around a negative source charge, they point inward. Between a positive and a negative charge, arrows point from the positive charge toward the negative charge.

A magnetic field is associated with magnets and electric currents. Outside a bar magnet, magnetic-field arrows point from north to south. If complete lines are drawn, they return through the magnet from south to north. Around a straight current-carrying wire, field lines form circles. Use the right-hand rule: point your right thumb along conventional current, the chosen current direction from positive toward negative, and your curled fingers show the magnetic-field direction.

A field line is a drawn line that shows the field’s local direction. At a point on a curved line, the direction follows the line’s tangent. In a qualitative diagram, closer line spacing represents a stronger field. The lines are not physical threads, and their count is not a measurement. In a diagram with several sources, arrows represent the field direction at each location.

\vec{g}: toward mass; \vec{E}: away from + and toward -; \vec{B}:N\to S outside a bar magnet

Mass: gravitational field arrows point toward the mass.
Electric charge: arrows point away from positive charge and toward negative charge.
Bar magnet: outside, arrows point north to south; through the magnet, they return south to north.
Closer field-line spacing indicates greater field strength qualitatively.

3. Draw and compare field diagrams

Start by labelling the source. Mark the mass, charge signs, magnet poles, or current direction. Then choose which field you are drawing. Do not apply one field’s direction rule to another.

For a single spherical mass or isolated charge, a simple sketch uses arrows along radial lines around the source. The arrows point inward for a mass, outward for a positive charge, and inward for a negative charge. These sketches compare directions, not numerical field values.

For a bar magnet, label both poles and draw outside arrows from north toward south. Include the return direction through the magnet if drawing complete lines. For a current-carrying wire, mark the current direction and use the right-hand rule to set the circular arrows. A dot represents current out of the page; a cross represents current into the page.

When comparing diagrams, ask the same questions for each: What is the source? What direction rule applies? Where do the arrows point? What does the spacing suggest? This keeps the comparison focused on sources and directions.

Label sources before drawing arrows.
Use the direction rule that matches the field.
Treat field diagrams as models, not photographs or motion paths.

Sources and field directions

Field	Source shown	Direction rule
Gravitational	Mass	Toward the mass
Electric	Electric charge	Away from positive; toward negative
Magnetic	Magnet or electric current	Outside a bar magnet, north to south; around a wire, use the right-hand rule

Worked example

Example 1: Field around a positive charge

Draw the direction pattern for the electric field around one isolated positive charge. Describe the field direction at a point to its left.

Set the system and viewpoint
The system is one positive source charge and the surrounding space. Use a page-fixed frame, with right chosen as the positive horizontal direction. The question asks for direction, not field strength.
Apply the electric-field rule
Electric-field direction is the direction a positive test charge would be pushed. A positive source repels a positive test charge, so arrows point away from the source on every side. \vec{E} points away from +
Read the direction on the left
At a point left of the source, away from the source means left. Since right is positive, the horizontal component is negative.
$E_x<0$

Answer: Draw radial arrows pointing outward from the positive charge. At a point to its left, the electric field points left.

Check: The direction matches the positive-charge rule. The negative horizontal sign is consistent with right chosen as positive.

Worked example

Example 2: Compare a mass and a negative charge

A mass and a negative charge are at the centres of separate sketches. Compare the field directions at points to the right of each source.

Set the comparison
Treat each sketch as a separate system, with its source fixed at the centre. Use the same page-fixed frame and choose right as positive in both sketches.
Determine the gravitational direction
A gravitational field around a mass points toward the mass. At a point to its right, toward the centre is left.
$\vec{g}\text{ points left}$
Determine the electric direction
An electric field around a negative charge points toward that charge. At a point to its right, toward the centre is also left.
$\vec{E}\text{ points left}$

Answer: Both arrows point left at the specified points. The sources and field types are still different: mass is the source of the gravitational field, and negative charge is the source of the electric field.

Check: Left is negative under the stated convention. Matching directions do not mean the fields have the same source or are the same physical quantity.

Worked example

Example 3: Magnetic field around a straight wire

A straight wire carries conventional current out of the page. Determine the magnetic-field direction at a point directly to the right of the wire.

Set the system and directions
The system is the current-carrying wire and its surrounding region. Use a page-fixed frame. The current is out of the page, represented by a dot; the point of interest is to the wire’s right.
Use the right-hand rule
Point your right thumb out of the page, along conventional current. Your fingers curl around the wire in the magnetic-field direction.
Read the direction on the right
On the right side of the wire, the curled fingers point upward on the page. Draw the circular field line with its arrow upward at that location.
$\vec{B}\text{ points upward}$

Answer: The magnetic field points upward at the point directly to the right of the wire.

Check: The direction follows the right-hand rule for current out of the page. Reversing the current reverses the field direction.

Common mistakes and how to avoid them

Drawing electric-field arrows toward a positive charge.

Correction: Arrows point away from a positive source and toward a negative source.

Drawing gravitational-field arrows away from a mass.

Correction: Around a mass, gravitational-field arrows point toward the mass.

Drawing magnetic arrows from south to north outside a bar magnet.

Correction: Outside the magnet, arrows go from north to south. The return direction is through the magnet from south to north.

Treating a field line as the route an object must follow.

Correction: A field line shows field direction at locations. It is not automatically an object’s path.

Assuming more drawn lines always mean a measured field value.

Correction: Line spacing can show relative strength qualitatively, but the drawing alone does not provide a numerical measurement.

Lesson summary

A field diagram represents field direction at different locations.
Gravitational fields point toward mass; electric fields point away from positive charge and toward negative charge.
Outside a bar magnet, magnetic-field arrows go from north to south. Around a current-carrying wire, use the right-hand rule.
Label sources and apply the matching direction rule before comparing diagrams.

Check your understanding

Question 1

At a point above an isolated negative charge, which way does the electric-field arrow point?

Up, away from the charge
Down, toward the charge
Right, regardless of the charge
It has no direction

Show answer and explanation

Down, toward the charge

Electric-field arrows point toward a negative source. From a point above it, toward the charge is downward.

Question 2

Outside a bar magnet, which direction do magnetic-field arrows show?

From south to north
From north to south
Toward the magnet’s centre from every direction
In the direction an iron object happens to move

Show answer and explanation

From north to south

Outside a bar magnet, the represented magnetic-field direction is from the north pole toward the south pole.

Question 3

What does an arrow on a field line indicate?

The speed of a test object
The local field direction
The source’s mass or charge value
The path every object will follow

Show answer and explanation

The local field direction

An arrow gives the field direction at that location. It does not give speed, source magnitude, or an object’s required path.

Key terms

Field: A description of how a source can influence objects or locations around it.
Field diagram: A visual model that uses lines and arrows to represent field directions and sometimes relative strength.
Field line: A drawn line whose local direction represents the field direction.
Test charge: A small positive charge used to define electric-field direction.
Conventional current: The chosen current direction from positive toward negative in a circuit; it sets the thumb direction in the wire right-hand rule.
Reference frame: The viewpoint and coordinate choices used to describe positions and directions.

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About this lesson and its review

Published by DoAssignment. This AI-assisted lesson follows Ontario Grade 12 Physics (SPH4U), expectation D3.3. 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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