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F2.5 · Investigate magnetic fields around conductors and solenoids

Learn to investigate magnetic fields around conductors and solenoids through clear examples and targeted practice.

Ontario Grade 11 Physics

Electricity and Magnetism

Ontario Grade 11 Physics — F2.5

A compass can turn near a current-carrying wire, even when no bar magnet is nearby. This gives evidence that a current is associated with a magnetic field. In this lesson, the physical system is a straight conductor or solenoid carrying current, together with the field around it. A magnetic field has strength and direction, so it is a vector. Current is a scalar quantity, but it has a stated direction in a circuit. We use conventional current: the direction positive charges would move. An investigation plan is a proposed procedure. It is not measured evidence until observations are collected.

What you will learn

1. Prerequisite bridge: current, compasses, and field diagrams

A circuit is a complete path through which electric charge can move. Current is the rate at which charge passes a point. Its SI unit is the ampere, written A\mathrm{A}. A source can drive current through a conducting wire when the circuit is complete.
A compass needle is a small magnet. Its north-seeking end points along the magnetic field at the compass. A field diagram uses lines and arrows to represent a field. By convention, the arrows show the direction a compass north pole would point. Lines are a model, not physical threads. In a simple diagram, closer lines can represent a stronger field.
The right-hand grip rule uses conventional current. For a wire viewed end-on, a dot, ⊙\odot, means current is toward the viewer. A cross, ⊗\otimes, means current is away from the viewer. These symbols represent directions in three dimensions on a flat page.

2. Field around a straight conductor

When current flows in a straight conductor, the magnetic field forms circular paths around the wire. The wire lies at the centre of these circles. The field wraps around the wire rather than pointing along it.
To predict the direction, point your right thumb along the conventional current. Your curled fingers show the direction of the magnetic field around the conductor. When current points toward you, the field is counterclockwise as you look at the page. When current points away from you, it is clockwise.
A labelled end-on diagram can show a dot at the centre for current toward the viewer and circular arrows around it for the field. If the current reverses, reverse every field arrow too. A compass needle should align with the local field direction. Earth’s magnetic field can also affect a compass, so its direction may influence observations.
I:⊙⇒B⃗:counterclockwiseI: \odot \quad\Rightarrow\quad \vec{B}: \text{counterclockwise}

3. Field around a loop and a solenoid

When a current-carrying wire is bent into a loop, the field patterns from different parts of the wire combine. Through the middle of the loop, the field points mainly in one direction. A solenoid is a coil made from many loops of conducting wire. Its field pattern is similar to that of a bar magnet. Inside the coil, the field is fairly even and the field lines are mostly parallel. Outside, the field curves around.
Use the right-hand grip rule to find a solenoid’s field direction. Curl the fingers of your right hand in the direction of conventional current around the turns. Your thumb points along the field inside the solenoid and toward its north end. The ends act like north and south poles. Reversing the current switches which end is north.
Compasses can be placed at several positions inside and outside a solenoid to investigate direction. Iron filings on a card near the coil can outline a field pattern when the card is tapped gently. Filings do not show the field’s arrow direction; use a compass for that. A proposed method does not establish a result. Record actual observations before describing them as evidence.
For a fair comparison, change one factor at a time. To investigate the effect of current, keep the coil shape, number of turns, and compass position fixed. To investigate the effect of turn count, keep the current and measurement setup fixed. A stronger current or more turns generally produces a stronger solenoid field. Compass direction alone does not give a numerical field strength.
curled fingers: I⇒thumb: B⃗inside\text{curled fingers: } I \quad\Rightarrow\quad \text{thumb: } \vec{B}_{\text{inside}}

4. Plan and interpret an investigation

Begin with a testable question, such as: How does reversing current change the compass direction near a straight wire? The independent variable is the factor deliberately changed. The dependent observation is what is recorded to see how it responds. Control conditions are the relevant parts of the setup kept the same.
For this question, reverse the current and keep the wire position, compass position, and compass distance fixed. Record the current direction and the direction in which each compass needle’s north end points. Compare those observations with the right-hand grip rule. Do not write an expected result as though it were a measured result.
If observations do not match a prediction, check the current direction, compass placement, nearby magnetic materials, and whether the needle can turn freely. Draw the conductor or coil, label conventional current, and add field arrows that agree with the observations. Keep predicted outcomes distinct from recorded evidence.
Use a low-voltage source and avoid leaving a wire connected for a long time because current can heat it. Follow the teacher’s safety instructions. Do not place a compass where the needle cannot move freely.

Worked example

Predicting a straight-wire field

A straight wire passes through a card. Conventional current flows toward you, out of the card. Predict the field direction when viewed from above the card.
  1. Set the viewpoint
    The system is the wire and its surrounding field. You are looking toward the card from above. The current points toward you, represented by a dot.
    I:⊙I: \odot
  2. Apply the grip rule
    Point your right thumb toward yourself along the current. Your curled fingers show the direction around the wire.
    B⃗:counterclockwise\vec{B}: \text{counterclockwise}
Answer: The magnetic field circles the wire counterclockwise as viewed from above the card.
Check: This direction matches current toward the viewer. If the current were reversed, the field would be clockwise.

Worked example

Finding a solenoid’s north end

Viewed from the left end of a solenoid, conventional current travels counterclockwise around its turns. Which end is north?
  1. Set the viewing direction
    The system is the current-carrying solenoid. Look directly at its left end. The stated counterclockwise direction is the current around the turns from that viewpoint.
    I:counterclockwiseI: \text{counterclockwise}
  2. Use the right-hand grip rule
    Curl your right-hand fingers in the direction of the current around the coil. Your thumb points along the field inside the solenoid and toward its north end. The inside field points toward the left end.
    B⃗inside:left\vec{B}_{\text{inside}}: \text{left}
Answer: The left end is north.
Check: The thumb points toward the viewed end, so that end is north. Reversing the current would make the left end south.

Worked example

Planning a fair solenoid comparison

A student wants to investigate whether adding turns strengthens a solenoid’s field. The student has a compass, a coil, and a variable current source. What should be kept the same, and what evidence should be recorded?
  1. Choose the changed factor
    The independent variable is the number of turns. Keep the current setting, coil shape, compass position, and compass orientation the same for each comparison. N: changed I: constant
  2. Record observations
    At the same compass location, record the needle’s response for each turn count. Do not claim a result before collecting observations. Compare the results only after performing the procedure.
    compass response at fixed position\text{compass response at fixed position}
Answer: Change the turn count while holding the current and measurement setup fixed. Record the compass response for each condition. More turns are predicted to produce a stronger field, but only collected observations are evidence.
Check: Changing the current at the same time would make it unclear which change affected the response. Compass direction alone does not provide a numerical field strength.

Common mistakes and how to avoid them

Drawing straight field lines along a straight current-carrying wire.
Correction: Draw circular field lines centred on the conductor.
Using the left hand or electron flow with the right-hand grip rule.
Correction: Use the right hand and conventional current direction.
Saying iron filings show which way the field points.
Correction: Filings show a field pattern, not its arrow direction. Use a compass to determine direction.
Calling a predicted result a measured result.
Correction: Label predictions clearly. Report evidence only after recording actual observations.

Lesson summary

Check your understanding

Question 1

A straight wire carries conventional current away from you. Viewed from your position, which way does its magnetic field circle?
  1. Clockwise
  2. Counterclockwise
  3. Straight toward you
  4. There is no field around the wire
Show answer and explanation
Clockwise
Point your right thumb away from you. Your curled fingers go clockwise from your viewing position.

Question 2

What does the thumb show when you use the right-hand grip rule for a solenoid?
  1. The direction of electron flow
  2. The magnetic field inside the solenoid and toward its north end
  3. The direction of the field outside every part of the coil
  4. The position of the compass
Show answer and explanation
The magnetic field inside the solenoid and toward its north end
Curl the right-hand fingers with conventional current around the turns. The thumb points along the inside field and toward the north end.

Question 3

A student changes both the number of coil turns and the current while comparing compass responses. What is the main problem?
  1. A compass cannot respond to a solenoid
  2. The field lines become scalar quantities
  3. The student cannot tell which changed factor caused the response difference
  4. The solenoid has no north or south end
Show answer and explanation
The student cannot tell which changed factor caused the response difference
A fair comparison changes one factor at a time. Otherwise, the effects of turn count and current cannot be separated.

Key terms

Conventional current
The direction positive charges would move in a circuit; this is the direction used with the right-hand grip rule.
Magnetic field
The region where a magnet or compass experiences a magnetic effect.
Solenoid
A coil made from many loops of conducting wire.
Independent variable
The factor deliberately changed during an investigation.
Dependent observation
The result recorded to see how it responds to a changed factor.

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Published by DoAssignment. This AI-assisted lesson follows Ontario Grade 11 Physics (SPH3U), expectation F2.5. 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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