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F2.7 · Investigate induction using Lenz’s law and the right-hand rule

Learn to investigate induction using lenz’s law and the right-hand rule through clear examples and targeted practice.

Ontario Grade 11 Physics

Electricity and Magnetism

Using Lenz’s law and the right-hand rule

A magnet and a coil can produce current without touching. The key feature is a change in the magnetic field through the coil. In this lesson, you will predict the induced magnetic field using Lenz’s law, then use the right-hand rule to predict the current direction. You will also plan an investigation and identify what its measurements could show.

What you will learn

1. Prerequisite bridge: fields, coils, and directions

A magnetic field is a region where a magnet or an electric current can exert a magnetic force. We draw field arrows to show its direction. An arrow points in the direction a north test pole would move. Magnetic field is a vector: it has both magnitude and direction. Current is a scalar quantity, which has magnitude but no direction as a vector. In a circuit, however, we track current direction using conventional current.
A coil is wire wound into one or more loops. The opening inside a loop has an area. A magnetic field passing through that area is described as a field through the coil. When the field through a coil changes, it can induce a voltage. If the wire makes a closed circuit, that voltage can drive an induced current. Induced means produced by a change. A galvanometer is a sensitive meter that detects a small current and shows its direction.
For direction sketches and examples, imagine looking directly at one face of a flat coil. Use the coil’s central axis as the reference direction. We choose a field toward you, out of the page, as positive. A field away from you, into the page, is negative. These choices are a sign convention. The physical prediction does not depend on which convention you choose, as long as you use it consistently.

2. Lenz’s law: oppose the change

Lenz’s law predicts the direction of the magnetic field made by an induced current. This induced field acts to oppose the change in magnetic field through the coil. It does not always point opposite to the external field. It opposes the change in that field.
Use this sequence. First, identify the external field through the coil. Next, decide whether its strength is increasing or decreasing. Then predict an induced field that opposes that change. Finally, use the right-hand rule to find the conventional current direction that makes the induced field.
For a coil, curl the fingers of your right hand in the direction of conventional current around the loops. Your extended thumb points along the coil’s magnetic field and toward the coil’s north face. Conventional current is the direction positive charge would move in a circuit. In a metal wire, electrons move the opposite way, but the right-hand rule here uses conventional current.
For example, if an external field into the page gets stronger, the induced field points out of the page. If the external field into the page gets weaker, the induced field points into the page. In the second case, the induced field tries to maintain the weakening field.

3. Plan an investigation of induction

A useful investigation uses a bar magnet, a coil, connecting wires, and a galvanometer. The physical system is these parts together. Keep the coil fixed and choose one viewing direction. Mark the coil face and the magnet’s north and south poles. Record which way the meter needle deflects during each trial. A needle deflection is measured evidence that current was induced. Its direction indicates the current direction for the meter’s particular connections.
Change one feature at a time. Move the north pole toward the coil, pause with the magnet held still, and then move it away. Repeat with the south pole. Keep the coil position, meter connections, and viewing direction unchanged. These instructions describe a proposed procedure, not completed measurements.
Before taking measurements, make predictions. For each movement, use Lenz’s law to predict the coil’s induced field. For instance, as a north pole approaches, the field through the coil changes. The coil’s near face must act like a north pole to oppose the approach. Then use the right-hand rule to predict the conventional current direction. When the magnet moves away instead, the change reverses, so the predicted current direction reverses.
A fair comparison needs consistent meter connections and viewing direction. If the meter leads are swapped, the same current can deflect the needle the other way. Record the setup and direction of magnet motion so you can interpret the evidence. A simulation can help you visualize a prediction, but simulated output is not measured evidence from a physical investigation.

4. A reliable direction-prediction method

A direction sketch can use a dot for a field toward you and a cross for a field away from you. Think of the dot as the tip of an arrow coming toward you. Think of the cross as the tail of an arrow moving away. Both symbols describe the field relative to the person viewing the coil.
Work through the prediction in order: identify the external field direction, decide whether it is increasing or decreasing, choose the induced field that opposes that change, and then apply the right-hand rule. For an induced field toward you, point your right thumb toward you. Your curled fingers show counterclockwise conventional current as viewed from that face. For an induced field away from you, the current is clockwise from that face.
Do not decide current direction from magnet motion alone. The magnet’s pole, the direction of motion, and the viewing face all matter. State these details, then state the change in external field, the induced field, and the current direction. This makes it easier to catch a viewpoint error.

Worked example

A north pole approaches

A bar magnet’s north pole moves toward a coil. Viewed from the magnet side, the magnet’s field through the coil points into the page and is increasing. Predict the coil’s induced field and conventional current direction.
  1. Set the viewpoint
    The system is the magnet and closed coil. Keep the stated magnet-side view. The external field points into the page, and its strength is increasing.
  2. Apply Lenz’s law
    The induced field must oppose the increase in the into-page external field. It therefore points out of the page.
    B⃗ind\vec{B}_{\mathrm{ind}}
  3. Apply the right-hand rule
    Point your right thumb out of the page. Your fingers curl counterclockwise from the stated viewing face, giving the conventional current direction.
    IconvI_{\mathrm{conv}}
Answer: The induced field points out of the page, and conventional current is counterclockwise as viewed from the magnet side.
Check: An approaching north pole increases the original field through the coil. The coil’s near face acts like a north pole to oppose the approach, consistent with the predicted out-of-page field. This is a direction prediction, so no numerical units or significant figures are needed.

Worked example

An into-page field weakens

A coil experiences an external magnetic field into the page. The field becomes weaker while the coil remains closed. Predict the induced field and current direction from the face you are viewing.
  1. Identify the change
    The external field points into the page, but its strength is decreasing. Lenz’s law responds to the decrease, not just to the original field direction.
  2. Predict the induced field
    The induced field tries to maintain the original into-page field. It therefore also points into the page.
    B⃗ind\vec{B}_{\mathrm{ind}}
  3. Find the current direction
    Point your right thumb into the page. Your curled fingers show clockwise conventional current from the viewing face.
    IconvI_{\mathrm{conv}}
Answer: The induced field points into the page, and conventional current is clockwise from the viewing face.
Check: The induced field points in the same direction as the weakening external field, so it resists the decrease. The direction is consistent with the stated viewpoint. From the opposite face, clockwise and counterclockwise descriptions would switch.

Worked example

Predicting a galvanometer response

You plan to move a south pole toward a coil, pause with it held still, and then move it away. Predict how the galvanometer responds during each part. Keep the meter connections and viewing direction fixed.
  1. During approach
    As the south pole approaches, the field through the coil changes. Lenz’s law predicts an induced field that opposes that change. The galvanometer should deflect while the magnet moves.
  2. While the magnet is still
    With the magnet held still, the field through the coil is no longer changing. No continuing induced current is expected, so the needle should return to its no-current position.
  3. During withdrawal
    Moving the magnet away reverses the change compared with approaching it. The induced current direction reverses, so the galvanometer should deflect in the opposite direction while the magnet moves.
Answer: Expect a deflection during approach, no continuing deflection while the magnet is held still, and an opposite deflection during withdrawal. The exact needle direction depends on the meter connections and viewpoint.
Check: This is a prediction for a proposed investigation, not reported experimental data. No numerical current or voltage is supplied, so numerical units and significant figures do not apply. The predicted pattern is consistent with Lenz’s law.

Common mistakes and how to avoid them

Thinking the induced field always points opposite to the external field.
Correction: It opposes the change. If the external field weakens, the induced field points in the same direction as the external field.
Using the right-hand rule before deciding what the induced field must be.
Correction: First use Lenz’s law to predict the induced field. Then use the right-hand rule to find the conventional current direction.
Giving a current direction for an approaching north pole without stating the viewpoint.
Correction: State the viewing face and the field direction through the coil. Clockwise and counterclockwise depend on the face you view.
Treating a meter deflection as a definite current direction without noting the meter leads.
Correction: The meter connections determine which needle direction corresponds to conventional current. Keep them fixed or record any changes.

Lesson summary

Check your understanding

Question 1

Viewed face-on, an external field into the page is getting stronger. What are the induced field and conventional current directions?
  1. Into the page and clockwise
  2. Out of the page and counterclockwise
  3. Out of the page and clockwise
  4. Into the page and counterclockwise
Show answer and explanation
Out of the page and counterclockwise
The induced field opposes the increase, so it points out of the page. With your right thumb out of the page, your fingers curl counterclockwise.

Question 2

A magnet is held still beside a coil. What should you expect for continuing induced current?
  1. A continuing current because a magnet is nearby
  2. No continuing current because the field through the coil is not changing
  3. A current that always points toward the magnet
  4. A current that alternates direction while the magnet is still
Show answer and explanation
No continuing current because the field through the coil is not changing
In this situation, induction depends on a changing field through the coil. Holding the magnet still produces no continuing change.

Question 3

An into-page external field through a coil is decreasing. Which way does the induced field point?
  1. Into the page, to oppose the decrease
  2. Out of the page, to oppose the original field
  3. It has no direction because the field is decreasing
  4. Its direction cannot be predicted without the magnet’s speed
Show answer and explanation
Into the page, to oppose the decrease
The induced field tries to maintain the weakening into-page field, so it points into the page.

Key terms

Magnetic field
A region where a magnet or current can exert a magnetic force. Its direction can be shown with arrows.
Induced current
Current produced in a circuit when the magnetic field through it changes.
Lenz’s law
The rule that an induced field opposes the change in magnetic field through a coil.
Conventional current
The direction positive charge would move in a circuit.
Galvanometer
A sensitive meter used to detect small currents and show their direction.

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Published by DoAssignment. This AI-assisted lesson follows Ontario Grade 11 Physics (SPH3U), expectation F2.7. 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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