---
title: "Statically and dynamically induced emf"
subject: "Electrical Machines I"
chapter: 1
key: "semester_4/electrical_machines_i:static-dynamic-induced-emf"
source: https://www.bctengineer.com/q/semester_4/electrical_machines_i/static-dynamic-induced-emf
site: BCT Engineering
---

# Statically and dynamically induced emf

Electrical Machines I · Chapter 1: Magnetic Circuits and Induction

- Asked in: 2076 Bhadra, 8 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_i/static-dynamic-induced-emf
- Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machines_i/chapter-1

## Question

What is meant by statically and dynamically induced emf? On what factors do these depend? Give practical example of each.

## Short answer

Dynamically induced emf is motional emf caused by conductor movement in a magnetic field (e = Blv sinθ), as in a DC generator. Statically induced emf results from time-varying flux linking a stationary conductor (e = N dφ/dt), as in a transformer or inductor.

## Answer

By Faraday's law an emf is induced in a conductor whenever the flux linking it changes. If the change is caused by **movement of the conductor** (or field) it is a **dynamically induced emf**; if the conductor and field are both still and the **flux itself changes with time**, it is a **statically induced emf**.

#### Dynamically induced (motional) emf

A conductor of length $l$ moving with velocity $v$ at angle $\theta$ to a field of flux density $B$ cuts flux and has an emf

$$
e = B\,l\,v\sin\theta \quad \text{V}
$$

Direction is given by Fleming's right-hand rule.

Depends on:
- flux density B,
- active length of conductor l,
- speed v,
- angle θ between the motion and the field (maximum at 90°).

**Example:** the armature conductors of a dc generator or the stator conductors of an alternator; the emf of a dc generator is $E = \frac{\phi Z N P}{60A}$.

#### Statically induced emf

The conductor is stationary and the flux linking it changes. Two kinds:

**(a) Self-induced emf:** emf induced in a coil by the change of its own current.

$$
e = -L\frac{di}{dt}, \quad L = \frac{N\phi}{I} = \frac{N^2}{S} = \frac{\mu_0\mu_r N^2 A}{l}
$$

Depends on the number of turns, the reluctance (core material, length, area) and the rate of change of current.
**Example:** the emf in a choke or the spark across a switch when an inductive circuit is opened.

**(b) Mutually induced emf:** emf induced in one coil by the change of current in a nearby coil.

$$
e_2 = -M\frac{di_1}{dt}, \quad M = k\sqrt{L_1L_2}
$$

Depends on the turns of both coils, the reluctance of the common path, the coupling coefficient $k$, and $di_1/dt$.
**Example:** the transformer, where an alternating primary current induces an emf in the secondary: $E = 4.44 f N \phi_m$.

#### Comparison

| Point | Dynamically induced | Statically induced |
|---|---|---|
| Cause | Relative motion of conductor and field | Time change of flux |
| Motion | Needed | No motion |
| Formula | $e = Blv\sin\theta$ | $e = N\,d\phi/dt$ |
| Energy conversion | Mechanical ↔ electrical | Electrical ↔ electrical |
| Example | DC generator, alternator | Transformer, inductor |

## Check yourself

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

1. A dynamically induced emf is produced when:
   A. Flux changes with time in a stationary coil
   B. A conductor moves relative to the field so it cuts flux
   C. Current is constant
   D. Two coils are stationary
   Answer: B. Motional emf arises from relative motion; statically induced emf comes from time-varying flux. (Key point: Definitions)

2. Dynamically induced emf e = B l v sin(theta) is a maximum when theta is:
   A. 0 degrees
   B. 45 degrees
   C. 90 degrees
   D. 180 degrees
   Answer: C. sin(theta) = 1 when the motion is perpendicular to the field. (Key point: Formula and factors)

3. Statically induced emf includes:
   A. Self and mutual induced emf
   B. Only motional emf
   C. Back emf only
   D. Eddy emf only
   Answer: A. Self-induced (own current change) and mutually induced (neighbouring coil) emfs are the two static types. (Key point: Static types)

4. Correct example pair is:
   A. Dynamic: transformer; static: dc generator
   B. Dynamic: dc generator / alternator; static: transformer / choke
   C. Both: transformer
   D. Dynamic: choke; static: alternator
   Answer: B. Machines with moving conductors are dynamic; transformers and chokes have stationary coils. (Key point: Examples)

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