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F3.2 · Use the right-hand rule for conductors and solenoids

Learn to use the right-hand rule for conductors and solenoids through clear examples and targeted practice.

Ontario Grade 11 Physics

Electricity and Magnetism

Finding magnetic-field directions from conventional current

A current-carrying conductor produces a magnetic field. A solenoid is a coil of wire, and its current also produces a magnetic field. In this lesson, you will use your right hand to connect conventional current direction to magnetic-field direction. The rule gives direction, not field strength.

The system in each example is the current-carrying wire or solenoid and the magnetic field it produces. Conventional current is the direction assigned to current in circuit diagrams. Follow that direction, not electron flow. A direction can depend on where you are looking from, so name the viewpoint when it matters.

What you will learn

Distinguish conventional current direction from magnetic-field direction.
Use the right-hand rule to find the field direction around a straight conductor.
Use the right-hand rule to identify a solenoid’s north pole and the field direction inside it.
State the viewpoint when describing directions into or out of the page, or clockwise or counterclockwise.

1. Prerequisite bridge: current, field, and direction

A scalar has size only. A vector has both size and direction. Current is measured in amperes (A), and an arrow can show its direction. Magnetic field is a vector. Here, we focus on its direction rather than its size. At a location, the magnetic-field direction is the direction a compass north end would point.

A straight conductor is a wire treated as straight over the part being considered. A solenoid is a coil of wire made from many loops. Each loop is called a turn. The field pattern around a straight conductor differs from the field pattern of a solenoid, so first identify which object you have.

For directions on a page, imagine looking straight at the page. A dot inside a circle,

\odot

, represents a direction coming out of the page toward you. A cross inside a circle,

\otimes

, represents a direction going into the page away from you. These symbols show direction, not size.

Use conventional current, not electron flow.
The right-hand rule predicts magnetic-field direction.
State the location or viewpoint when it affects the direction description.

2. Straight conductors: the curled-fingers rule

For a straight current-carrying conductor, point your right thumb along the conventional current. Curl your fingers around the wire. Your curled fingers show the magnetic-field direction around it.

Use the location named in the question. For a horizontal wire on the page with current to the right, the field at a point above the wire comes out of the page. At a point below the wire, it goes into the page. The direction changes around the wire, so do not assign one direction to every point.

You can check the rule by imagining your hand wrapped around the wire. Keep your thumb aligned with the current, then follow the direction your fingers curl at the point being considered.

\text{thumb} \parallel I,\quad \text{curled fingers} \parallel \vec{B}

Thumb: conventional current in the wire.
Curled fingers: magnetic-field direction around the wire.
For current to the right, the field is out of the page above the wire and into the page below it.

3. Solenoids: the grip rule

For a solenoid, curl the fingers of your right hand in the direction of conventional current around the turns. Your extended thumb points toward the solenoid’s north pole. It also points in the magnetic-field direction inside the solenoid.

Imagine looking straight at one end of the coil. If the current appears to circle counterclockwise from that end, that end is north. If the current appears clockwise, that end is south. The viewpoint matters: from the opposite end, the current appears to circle the other way, but the physical poles do not change.

The two hand positions answer different questions. For a straight wire, the thumb follows current and the curled fingers show the field. For a solenoid, the curled fingers follow current around the turns and the thumb identifies the north-pole direction.

\text{fingers} \parallel I_{\text{turns}},\quad \text{thumb} \parallel \vec{B}_{\text{inside}}

Solenoid fingers: conventional current around the turns.
Solenoid thumb: north pole and field direction inside the coil.
State which end you are viewing before using clockwise or counterclockwise.

4. A reliable method and a reasonableness check

First name the object: straight conductor or solenoid. Then state the conventional-current direction and the viewpoint. For a straight wire, point your thumb along the current and check the field at the location named in the question. For a solenoid, curl your fingers with the current around the turns and use your thumb to identify the north-pole direction.

A right-hand-rule question is usually a direction question. It does not call for a numerical field calculation or significant figures. Current is measured in amperes (A), and magnetic field is measured in teslas (T), but do not invent a field magnitude when only direction is requested.

Check that your hand position matches the object and current. For a straight wire, check the field at the stated location. For a solenoid, check which end you are viewing. A useful reasonableness check is to reverse the current mentally: the field or pole direction should reverse as well.

Match the rule to the object.
Use conventional current and the stated viewpoint.
Report a direction, not an unsupported field value.

Worked example

Field above a straight wire

A straight wire lies horizontally on the page. Conventional current flows to the right. What is the magnetic-field direction at a point above the wire?

Set the direction
The system is the wire and its magnetic field. The page is the viewing plane, and the point is above the wire. Take right as the positive direction along the wire; the current points in that direction.
Apply the conductor rule
Point your right thumb to the right along the current. Curl your fingers around the wire. At the point above the wire, the curl points out of the page, toward the viewer.
$\vec{B}:\ \odot$

Answer: The magnetic field above the wire points out of the page, toward the viewer.

Check: The thumb follows the stated current. The field direction is for the point above the wire, not for every point around it. This is a direction result, so no numerical value or unit calculation is needed.

Worked example

Field below a straight wire

A straight wire lies horizontally on the page. Conventional current flows to the left. What is the magnetic-field direction at a point below the wire?

Set the direction
The system is the wire and the point below it. Use the page as the viewing plane and take left as the current direction along the wire.
Apply the conductor rule
Point your right thumb to the left. Curl your fingers around the wire. At a point below it, the curl points out of the page, toward the viewer.
$\vec{B}:\ \odot$

Answer: The field below the wire points out of the page, toward the viewer.

Check: At a fixed location, reversing the current reverses the field direction. For current to the right, the field below the wire is into the page; with current to the left, it is out of the page. No field magnitude is given or needed.

Worked example

Identify a solenoid end

You look straight at the left end of a solenoid. From your viewpoint, conventional current around the turns appears clockwise. Which pole is at the left end?

Fix the viewpoint
The system is the solenoid. The viewpoint is straight at its left end. This matters because clockwise and counterclockwise depend on which end you view.
Use the solenoid rule
Curl your right-hand fingers in the clockwise direction seen from that end. Your thumb points away from you, into the solenoid. The thumb points toward the north pole, so the viewed left end is the south pole.

Answer: The left end is the south pole.

Check: If the current appeared counterclockwise from this same viewpoint, the thumb would point toward the viewer and that end would be north. The stated clockwise direction therefore makes the left end south.

Common mistakes and how to avoid them

Using the left hand or pointing the thumb opposite to conventional current.

Correction: Use your right hand. For a straight conductor, point the thumb along conventional current before reading the curled fingers.

Saying that the field points in one direction everywhere around a straight wire.

Correction: The curled fingers show a field direction around the wire. Check the location named in the question, such as above or below it.

Calling a solenoid end north from clockwise current without stating which end is viewed.

Correction: State the viewpoint. The current appears clockwise from one end and counterclockwise from the opposite end.

Using electron flow instead of conventional current.

Correction: Use the conventional-current direction shown by the arrow in a circuit diagram.

Lesson summary

Use conventional current for both right-hand rules.
For a straight conductor, the thumb follows current and curled fingers show the field around the wire.
For a solenoid, fingers follow current around the turns; the thumb points toward the north pole and along the field inside.
Identify the object, current direction, location, and viewpoint before stating a field direction.

Check your understanding

Question 1

A straight wire runs left to right, with conventional current to the right. What is the field direction at a point below the wire?

Into the page
Out of the page
Toward the right
Toward the left

Show answer and explanation

Into the page

Point your right thumb to the right along the current and curl your fingers around the wire. At a point below the wire, the field points into the page.

Question 2

You view one end of a solenoid and see the conventional current moving counterclockwise around its turns. What is that end?

North
South
Neither pole
It cannot be identified without a current magnitude

Show answer and explanation

North

Curl your right-hand fingers counterclockwise as viewed from that end. Your thumb points toward you, identifying that end as north.

Question 3

For a straight conductor, what does the thumb represent when using the right-hand rule?

The magnetic-field direction at every point
The direction of conventional current
The direction of electron flow
The direction toward the solenoid’s north pole

Show answer and explanation

The direction of conventional current

For a straight conductor, the thumb follows conventional current. The curled fingers show the magnetic-field direction around the wire.

Key terms

Conventional current: The assigned direction of current used in circuit diagrams and in these right-hand rules.
Magnetic field: A region where magnetic effects can be detected; its direction at a location is the direction a compass north end points.
Solenoid: A coil of wire made from many turns.
Vector: A quantity with both size and direction.
Scalar: A quantity with size but no direction.
North pole: The solenoid end toward which the right-hand-rule thumb points when the fingers follow conventional current around the turns.

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About this lesson and its review

Published by DoAssignment. This reviewed lesson follows Ontario Grade 11 Physics (SPH3U), expectation F3.2. It is a study resource, not an official curriculum publication.

Before publication, content is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability. Errors can still occur, so corrections are welcomed.

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