---
title: "Faraday's laws; static and dynamic emf"
subject: "Electrical Machine"
chapter: 1
key: "semester_4/electrical_machine:faraday-static-dynamic-emf"
source: https://www.bctengineer.com/q/semester_4/electrical_machine/faraday-static-dynamic-emf
site: BCT Engineering
---

# Faraday's laws; static and dynamic emf

Electrical Machine · Chapter 1: Magnetic Circuits and Induction

- Asked in: 2071 Magh, 6 marks
- Video: [Statically and Dynamically Induced EMF | Exam Pointer Series](https://www.youtube.com/watch?v=If_o27kxxBU) — TechInsight
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/electrical_machine/faraday-static-dynamic-emf
- Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machine/chapter-1

## Question

State Faraday's Laws of electromagnetic induction. Distinguish between statically induced emf and dynamically induced emf.

## Short answer

Faraday's first law: changing flux linkage induces emf. Second law: e = -N dφ/dt. Statically induced emf arises from time-varying flux with stationary conductor (e = -N dφ/dt), e.g., transformer. Dynamically induced emf arises from conductor moving through a magnetic field (e = B l v sinθ), e.g., generator.

## Answer

#### Faraday's laws
1. **First law:** whenever the flux linked with a circuit changes, an emf is induced in it. The emf exists only while the flux is changing.
2. **Second law:** the magnitude of the induced emf equals the rate of change of flux linkage:  **e = −N dφ/dt** (volts). The negative sign (Lenz's law) shows that the emf opposes the change causing it.

#### Statically and dynamically induced emf
| Basis | Statically induced emf | Dynamically induced emf |
|---|---|---|
| Cause | Flux changes with time, conductor is stationary | Conductor cuts a stationary field (or field moves past conductor) |
| Formula | e = −N dφ/dt | e = B l v sin θ |
| Sub-types | Self-induced and mutually induced | Motional emf |
| Example | Transformer windings, inductor coils | DC/AC generator armature conductors |
| Moving part | None | Conductor or magnet must move |
| Direction found by | Lenz's law | Fleming's right-hand rule |

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. In statically induced emf, what is true?
   A. The conductor moves through a fixed field
   B. Only a generator can produce it
   C. The flux changes with time while the conductor is stationary
   D. It is found by Fleming's right-hand rule
   Answer: C. Static emf arises when the flux varies in time with no motion, as in a transformer; formula e = -N dphi/dt. (Key point: Static emf)

2. Which expression gives dynamically induced emf?
   A. e = I R
   B. e = B l v sin(theta)
   C. e = -N dphi/dt
   D. e = L di/dt
   Answer: B. Motional (dynamic) emf is e = B l v sin(theta), found by Fleming's right-hand rule. (Key point: Dynamic emf)

3. Which pair is correctly matched?
   A. Transformer windings: static; generator armature conductors: dynamic
   B. Both are dynamic
   C. Transformer windings: dynamic; generator conductors: static
   D. Both are static
   Answer: A. Transformer emf is statically induced; generator armature conductors cut the field, giving dynamic emf. (Key point: Examples)

4. What does Faraday's second law say?
   A. Induced emf equals the flux
   B. Emf is independent of time
   C. Induced emf equals the rate of change of flux linkage
   D. Emf is produced only by motion
   Answer: C. e = -N dphi/dt in magnitude: rate of change of flux linkage. (Key point: Second law)

## Related in Electrical Machine

- [Faraday laws; static vs dynamic emf](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Afaraday-static-dynamic-emf) — Electrical Machines, chapter 1
- [Statically and dynamically induced emf](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Astatic-dynamic-induced-emf) — Electrical Machines I, chapter 1
- [Soft magnetic material, Faraday's laws](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Asoft-magnetic-faraday-laws) — Electrical Machines, chapter 1
- [Faraday's laws; Fleming's rules](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machine%3Afaraday-fleming-rules) — Electrical Machine, chapter 1

## Related in other subjects

- [Faraday's laws; mechanical to heat energy](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Afaraday-law-mechanical-to-heat) — Engineering Physics, chapter 8