# Electromagnetic Induction and Faraday's Law

Physics I · Principles of Electromagnetism and Optics · https://tryals.app/learn/physics-i/electromagnetic-induction-and-faradays-law

## Faraday's Law & Flux

Move a magnet near a coil and current flows: mechanical motion transmuted into electricity. A changing magnetic flux through a loop induces an **EMF** (voltage):

$$\varepsilon = -\frac{d\Phi_B}{dt}, \qquad \Phi_B = \int_S \vec{B}\cdot d\vec{A}$$

| Quantity | Symbol | SI Unit |
| --- | --- | --- |
| Magnetic flux | $\Phi_B$ | Wb |
| EMF | $\varepsilon$ | V |
| Inductance | $L$ | H |

The minus sign is **Lenz's law**: induced currents always fight the change that made them.

**Ways to change flux:** Change $B$ (field strength), change $A$ (loop area), or change $\theta$ (loop orientation).

## EMF, Inductance & Pitfalls

**Motional EMF** occurs when a conductor of length $L$ moves at velocity $v$ through a field $B$:

$$\varepsilon = BLv$$

**Self-inductance** ($L$) measures how a coil opposes changes in its own current:

$$\varepsilon = -L\frac{dI}{dt}, \qquad U = \frac{1}{2}LI^2$$

where $U$ is the energy stored in an inductor and $L = N\Phi_B / I$.

> **Common pitfall:** Induction responds to **changing flux**, not to flux itself. A coil soaked in a steady field induces zero voltage; only a wobbling field creates an EMF.

## Practice questions

4 of this lesson's 11 practice questions, with answers. The full set is in the app.

### 1. Which can cause an induced EMF in a loop?

A. Rotating the loop in a uniform B
B. Changing the magnetic field strength
C. Having a constant B through a stationary loop
D. Changing the area of the loop

**Answer:** A. Rotating the loop in a uniform B; B. Changing the magnetic field strength; D. Changing the area of the loop

**Why:** EMF requires a change in flux $\Phi = BA \cos$ $\theta$; any variable can change.

Page: https://tryals.app/practice/physics-i/electromagnetic-induction-and-faradays-law/which-can-cause-an-induced-emf-in-a-loop

### 2. Sort: Faraday's law application or not?

**Answer:**

- Faraday's law: Electric generator, Transformer, Induction cooktop, Magnetic braking
- Not Faraday's law: Battery, Resistor

**Why:** Generators, transformers, induction cooking, and magnetic brakes all use electromagnetic induction.

Page: https://tryals.app/practice/physics-i/electromagnetic-induction-and-faradays-law/sort-faradays-law-application-or-not

### 3. You drop a strong magnet down a **copper pipe** (copper is not magnetic). The magnet falls strangely slowly. Why?

A. Air is compressed ahead of the magnet in the pipe
B. Falling flux induces eddy currents opposing the motion
C. Copper is weakly ferromagnetic after all
D. The magnet magnetizes the pipe permanently and sticks to it

**Answer:** B. Falling flux induces eddy currents opposing the motion

**Why:** Each pipe section experiences changing flux, driving circular eddy currents that create fields opposing the magnet’s motion, braking it. No contact, no friction: this is exactly how magnetic brakes on roller coasters and high-speed trains work.

Page: https://tryals.app/practice/physics-i/electromagnetic-induction-and-faradays-law/you-drop-a-strong-magnet-down-a-copper-pipe-copper-is-not-magnetic

### 4. Lenz’s law says the induced current opposes the change producing it. What goes wrong if it reinforced the change instead?

A. The magnetic field would become infinite, which is geometrically impossible
B. The current would flow in the wrong direction around the loop
C. Nothing physical; the sign is a convention about which way is positive
D. Energy would appear from nothing, so the sign is conservation

**Answer:** D. Energy would appear from nothing, so the sign is conservation

**Why:** Reinforcement would be a runaway. The minus sign in Faraday’s law is not bookkeeping, it is what stops the universe containing free-energy machines.

Page: https://tryals.app/practice/physics-i/electromagnetic-induction-and-faradays-law/lenzs-law-says-the-induced-current-opposes-the-change-producing-it