---
title: "Faraday laws; static vs dynamic emf"
subject: "Electrical Machines"
chapter: 1
key: "semester_4/electrical_machines:faraday-static-dynamic-emf"
source: https://www.bctengineer.com/q/semester_4/electrical_machines/faraday-static-dynamic-emf
site: BCT Engineering
---

# Faraday laws; static vs dynamic emf

Electrical Machines · 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_machines/faraday-static-dynamic-emf
- Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machines/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: emf is induced when flux linking a coil changes. Second law: magnitude = N dφ/dt, direction opposes the cause (Lenz's law, e = –N dφ/dt). Statically induced emf arises from time-varying flux without motion (e = –N dφ/dt); dynamically induced emf from conductor moving in steady field (e = Blv sinθ). The former occurs in transformers, the latter in generators.

## Answer

#### Faraday's laws of electromagnetic induction

1. **First law:** when the magnetic flux linked with a coil or conductor changes, an emf is induced in it. There is no emf while the flux is constant.
2. **Second law:** the magnitude of the induced emf equals the rate of change of flux linkages, $e = N\dfrac{d\phi}{dt}$. The direction is given by Lenz's law, which opposes the cause of the change, hence $e = -N\dfrac{d\phi}{dt}$.

#### Statically induced emf vs dynamically induced emf

| Point | Statically induced emf | Dynamically induced emf |
|---|---|---|
| Cause | Flux changes with time while the coil is stationary | Conductor moves in a steady field, cutting the flux |
| Formula | $e = -N\,d\phi/dt$ | $e = Blv\sin\theta$ |
| Motion | No relative motion needed | Relative motion between field and conductor is essential |
| Types | Self-induced and mutually induced | Single type (motional emf) |
| Example | Transformer, inductor | Generator, alternator |
| Direction rule | Lenz's law | Fleming's right-hand rule |
| Source of flux | Alternating or varying current | Usually a steady field (dc excitation) |

## Check yourself

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

1. According to Faraday's first law, when is emf induced?
   A. When flux linked with the coil is constant
   B. When flux linked with the coil changes
   C. When current is large
   D. Only when the coil moves
   Answer: B. A change of linked flux induces emf, which lasts only while the flux changes. (Key point: First law)

2. What does the negative sign in e = -N d(phi)/dt show?
   A. Emf is always negative
   B. Induced emf opposes the change that causes it
   C. Flux is decreasing
   D. Emf is dc
   Answer: B. Lenz's law gives the direction: the emf opposes the cause. (Key point: Lenz's law)

3. What distinguishes statically from dynamically induced emf?
   A. Static: flux varies with a stationary coil; dynamic: conductor moves in a steady field
   B. Static: conductor moves; dynamic: coil stationary
   C. Both need relative motion
   D. Static uses dc only
   Answer: A. Static emf comes from time-varying flux; dynamic emf from conductor motion cutting flux. (Key point: Static vs dynamic cause)

4. Which pairing of emf type and device is right?
   A. Static - generator, dynamic - transformer
   B. Static - transformer, dynamic - generator
   C. Both - transformer
   D. Both - generator
   Answer: B. Transformer action is static emf; generators use motional emf. (Key point: Examples)

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