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Lenz's Law

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Topic: Electromagnetism > Electromagnetic Induction > Lenz's Law

1. Core Definition: Lenz's Law

**Lenz's Law** determines the **direction** of induced current.

* **Core Content**: The direction of the induced current is such that its magnetic field **opposes** the **change in magnetic flux** that produced it.

* **Physical Essence**: A manifestation of **Conservation of Energy**. The energy of the induced current comes from work done against this "opposing" force.

**Key Mnemonics (Memorize these!)**:

1. **"Increase-Opposite, Decrease-Same"**: Flux increases $\rightarrow$ Induced B-field is **Opposite** to original B; Flux decreases $\rightarrow$ Induced B-field is **Same** direction as original B.

2. **"Come-Reject, Go-Retain"**: Magnet approaches $\rightarrow$ Repel (Reject); Magnet moves away $\rightarrow$ Attract (Retain).

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2. The Four-Step Method

Standard procedure for flux change in loops.

1. **Original Field**: Identify direction of original magnetic field ($B_{orig}$).

2. **Change**: Determine if flux ($\Phi$) is **Increasing** or **Decreasing**.

3. **Induced Field** (Key): Use **"Increase-Opposite, Decrease-Same"** to find direction of Induced Field ($B_{ind}$).

4. **Current**: Use **Ampere's Right-Hand Grip Rule** to find Induced Current ($I_{ind}$) based on $B_{ind}$.

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3. Alternative: Conductor Cutting Field Lines

When a conductor cuts magnetic field lines, Lenz's Law implies: **The Ampere force on the induced current opposes the relative motion.**

Use **Fleming's Right-Hand Rule** for speed (Generator Rule):

* **Usage**: Generators, Motion-induced EMF.

* **Gesture**: Open Right Hand. Field ($B$) pierces palm. Thumb points to Motion ($v$). Fingers point to Induced Current ($I$).

| Rule Confusion | English Name | Usage | Device |

| :--- | :--- | :--- | :--- |

| **Ampere's Rule** (Grip) | Right-Hand Grip Rule | $I \leftrightarrow B$ | Solenoid |

| **Right-Hand Rule** (Palm) | Fleming's Right-Hand Rule | $v + B \rightarrow I$ | Generator |

| **Left-Hand Rule** (Palm) | Fleming's Left-Hand Rule | $I + B \rightarrow F$ | Motor |

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4. Typical Examples

**Example 1: Applying "Increase-Opposite"**

**Problem**: A bar magnet (N pole down) moves down into a metal ring. Find current direction (Top view).

**Solution**:

1. **Original B**: Down.

2. **Change**: Magnet enters $\rightarrow$ Downward flux **Increases**.

3. **Oppose**: Induced B must be **Up** (Opposite).

4. **Current**: Right-Hand Grip Rule, Thumb Up $\rightarrow$ Fingers **Counter-Clockwise**.

**Answer**: Counter-Clockwise.

**Example 2: Applying "Come-Reject"**

**Problem**: In Example 1, does the ring shrink or expand? What is the force direction on the ring?

**Solution**:

* **Force**: "Come-Reject". Magnet approaches, ring repels it. Force on ring is **Down**.

* **Deformation**: "Increase-Shrink". Flux increases, ring tends to **Shrink** to minimize flux.

**Example 3: Cutting Field**

**Problem**: Rod moves Right cutting B-field (Into page). Find current direction.

**Solution**:

Use **Fleming's Right-Hand Rule**:

* Field into palm (Palm faces Out).

* Thumb points Right (Velocity).

* Fingers point **Up**.

**Answer**: Current flows Upward.