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Electromagnetic Induction

CSCA Electromagnetic Induction study guide organized around the publicly available CSCA syllabus. Practice Physics questions on aicsca.com.

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Topic: Electromagnetism > Electromagnetic Induction

1. Core Concept: Magnetism produces Electricity

**Electromagnetic Induction** is the phenomenon where an electric current (induced current) is generated in a closed circuit whenever the **magnetic flux through it changes**.

**CSCA Exam Focus**:

* **Condition**: Key is $\Delta \Phi \neq 0$ (Change in Flux).

* **Two Fundamental Laws**:

1. **Faraday's Law**: Calculates Magnitude (How much?).

2. **Lenz's Law**: Determines Direction (Which direction?).

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2. Quantitative Calculation: Faraday's Law

(1) Flux Change Type

General case where magnetic field or area changes.

$$ \mathcal{E} = N \frac{\Delta \Phi}{\Delta t} $$

* $\mathcal{E}$: Induced EMF (V).

* $N$: Number of turns.

* $\frac{\Delta \Phi}{\Delta t}$: **Rate of change** of flux (Wb/s).

(2) Cutting Magnetic Lines Type

Conductor moving through a magnetic field.

$$ \mathcal{E} = B L v \sin\theta $$

* $L$: **Effective cutting length** (m).

* $v$: Relative velocity (m/s).

* $\theta$: Angle between velocity $\vec{v}$ and field $\vec{B}$.

* **$v \perp B$ ($\\theta=90^\circ$)**：$\mathcal{E} = BLv$ (**Most Common**).

* **$v \parallel B$ ($\\theta=0^\circ$)**：$\mathcal{E} = 0$ (No cutting).

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3. Direction Judgment: Lenz's Law & Right-Hand Rule

Be sure to distinguish which hand to use for "Force" vs. "Current"!

| Rule | Usage | Scenario |

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

| **Lenz's Law** | Direction of Induced Current | General (Flux Change) |

| **Right-Hand Rule** | Direction of Induced Current | **Cutting Lines ONLY** |

(1) The "Opposition" Philosophy of Lenz's Law

**Key Mnemonic: Increase-Oppose, Decrease-Same**.

* **Increase**: Original flux $\uparrow$ $\rightarrow$ Induced B-field **Opposite** to Original B (Oppose increase).

* **Decrease**: Original flux $\downarrow$ $\rightarrow$ Induced B-field **Same** as Original B (Oppose decrease).

(2) Right-Hand Rule (Generator Rule)

**Open Right Hand**:

* Magnetic Field ($B$) **pierces palm**.

* **Thumb** points to **Motion** ($v$).

* **Fingers** point to **Induced Current** ($I$).

**Tip**: **Left-Force, Right-Electricity**. Use Left Hand for Forces (Motors), Right Hand for Induction (Generators).

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4. Typical Examples

**Example 1: Faraday's Law**

**Problem**: A 100-turn coil, area $0.1 m^2$, perpendicular to B-field. B increases from $0.1T$ to $0.5T$ in $2s$. Find EMF.

**Solution**:

$$ \mathcal{E} = N \frac{\Delta \Phi}{\Delta t} = N \frac{(B_2 - B_1)S}{\Delta t} $$

$$ \mathcal{E} = 100 \times \frac{(0.5 - 0.1) \times 0.1}{2} = 100 \times \frac{0.04}{2} = 2 V $$

**Example 2: Lenz's Law**

**Problem**: A bar magnet (N pole down) is dropped into a coil. Viewed from above, is the induced current clockwise or counter-clockwise?

**Solution**:

1. **Original B**: Down (N pole).

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

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

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

**Answer**: Counter-Clockwise.

**Example 3: Cutting Lines & Force**

**Problem**: Wire $L=0.5m$ moves at $v=4m/s$ perpendicular to $B=0.5T$. Resistance $R=0.2\Omega$. Find: (1) EMF; (2) Current; (3) Pulling Force for constant speed.

**Solution**:

(1) $\mathcal{E} = BLv = 0.5 \times 0.5 \times 4 = 1 V$.

(2) $I = \mathcal{E}/R = 1 / 0.2 = 5 A$.

(3) Ampere's Force $F_A = BIL = 0.5 \times 5 \times 0.5 = 1.25 N$.

Constant speed $\rightarrow$ Pulling Force $F_{pull} = F_A = 1.25 N$.

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5. CSCA Common Pitfalls

1. **Flux Calculation**: In $\Phi = BS \cos\theta$, $\theta$ is the angle between the **Normal** and B-field. If given angle $\alpha$ between Coil Plane and B, use $\sin\alpha$.

2. **EMF vs Current**: Cutting lines always creates EMF (like a battery), but Current flows only if the circuit is **closed**.

3. **Right Hand vs Left Hand**:

* Find **Induced EMF/Current** (Generator) $\rightarrow$ **Right Hand**.

* Find **Magnetic Force/Motion** (Motor) $\rightarrow$ **Left Hand**.