---
title: "Soft magnetic material, Faraday's laws"
subject: "Electrical Machines"
chapter: 1
key: "semester_4/electrical_machines:soft-magnetic-faraday-laws"
source: https://www.bctengineer.com/q/semester_4/electrical_machines/soft-magnetic-faraday-laws
site: BCT Engineering
---

# Soft magnetic material, Faraday's laws

Electrical Machines · Chapter 1: Magnetic Circuits and Induction

- Asked in: 2071 Magh (old course), 10 marks
- Video: [Faraday's Law of Electromagnetic Induction, Magnetic Flux & Induced EMF - Physics & Electromagnetism](https://www.youtube.com/watch?v=LDOa7UdfcMQ) — The Organic Chemistry Tutor
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/electrical_machines/soft-magnetic-faraday-laws
- Whole chapter: https://www.bctengineer.com/md/semester_4/electrical_machines/chapter-1

## Question

Why soft magnetic material is used to make transformer core or armature core of the electrical equipment? State and explain Faraday's laws of electromagnetic induction. Describe different processes of EMF induced in a coil.

## Short answer

Soft magnetic materials have narrow hysteresis loop (low hysteresis loss), high permeability, low coercivity and retentivity, and high resistivity to reduce eddy currents. Faraday's first law: changing flux linkage induces emf. Second law: magnitude = N dφ/dt, direction given by Lenz's law (e = –N dφ/dt). Emf can be statically induced by time-varying flux (self or mutual) or dynamically induced by motion in a steady field (e = Blv).

## Answer

#### Why soft magnetic material is used for cores

Cores of transformers and armatures carry alternating flux, so in every cycle the material goes round its $B$–$H$ loop. Soft magnetic materials (silicon steel, soft iron, CRGO) are chosen for the following reasons.

- They have a **narrow hysteresis loop**, so the hysteresis loss (loop area $\times f\times V$) is small.
- They have **high permeability**, so a large flux is set up by a small magnetising current.
- They have **low coercivity and low retentivity**, so they magnetise and demagnetise easily without keeping residual magnetism.
- Silicon raises their **resistivity**, which lowers eddy current loss when the core is laminated.

#### Faraday's laws of electromagnetic induction

1. **First law:** whenever the flux linked with a coil changes, an emf is induced in it. The emf lasts only while the flux is changing.
2. **Second law:** the magnitude of the induced emf is equal to the rate of change of flux linkages:

$$
e = -N\frac{d\phi}{dt}
$$

The negative sign is Lenz's law: the induced emf drives a current that opposes the change that produced it.

#### Ways of inducing emf in a coil

1. **Statically induced emf:** the coil is at rest and the flux linking it changes with time.
   - *Self-induced:* the coil's own current changes, $e = -L\,di/dt$.
   - *Mutually induced:* the flux of a neighbouring coil changes, $e = -M\,di/dt$ (transformer action).
2. **Dynamically induced emf:** the flux is constant, but the coil moves across the field (or the field moves across the conductor). For a conductor of length $l$ moving with velocity $v$ at right angles to field $B$,

$$
e = Blv\ \text{volt}
$$

   This is the principle of generators. A combination of both is also possible, for example a moving coil in a time-varying field.

## Check yourself

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

1. Why is soft magnetic material used for transformer cores?
   A. Wide hysteresis loop for stored energy
   B. High retentivity to keep flux
   C. Narrow loop, high permeability and low coercivity give low loss
   D. Low resistivity to carry current
   Answer: C. A narrow loop gives low hysteresis loss, and high permeability needs a small magnetising current. (Key point: Why soft magnetic cores)

2. What does Faraday's second law state?
   A. Induced emf is proportional to flux
   B. Induced emf equals the rate of change of flux linkages
   C. Induced emf is constant for constant flux
   D. Induced emf opposes the current
   Answer: B. e = -N d(phi)/dt, with the sign from Lenz's law. (Key point: Faraday second law)

3. Which is a statically induced emf?
   A. Conductor cutting a steady field
   B. Rotating armature of a generator
   C. Mutually induced emf in a transformer secondary
   D. Motional emf e = Blv
   Answer: C. The coil is at rest and the flux changes with time, as in transformer action. (Key point: Statically induced emf)

4. A conductor of length l moves at speed v at right angles to field B. The emf is?
   A. e = Blv
   B. e = Bl/v
   C. e = B v / l
   D. e = -L di/dt
   Answer: A. Flux cutting by a moving conductor gives e = Blv, the principle of generators. (Key point: Dynamically induced emf)

## Related in Electrical Machines

- [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
- [Inductance and average induced emf of iron ring coil](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Airon-rod-ring-inductance-average-emf) — Electrical Machines I, chapter 1
- [Two-coil magnetic circuit, current for 1.2 T](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Atwo-coil-core-1-2t-current) — Electrical Machines, chapter 1
- [Coil current for flux in three-limb cast steel core](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Acast-steel-three-limb-current) — Electrical Machines I, chapter 1
- [Coil current for 2 mWb in central limb of core](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines_i%3Athree-limb-two-coils-central-core) — Electrical Machines I, chapter 1
- [Three-coil core, flux in air gap](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machines%3Athree-coil-core-airgap-flux) — Electrical Machines, chapter 1

## Related in other subjects

- [Faraday's laws; static and dynamic emf](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machine%3Afaraday-static-dynamic-emf) — Electrical Machine, chapter 1
- [Magnetic material for electromagnetic relays](https://www.bctengineer.com/question.md?key=semester_3%2Felectrical_engineering_material%3Arelay-magnetic-material) — Electrical Engineering Material, chapter 4
- [Faraday's laws; Fleming's rules](https://www.bctengineer.com/question.md?key=semester_4%2Felectrical_machine%3Afaraday-fleming-rules) — Electrical Machine, chapter 1
- [Requirements of transformer core material](https://www.bctengineer.com/question.md?key=semester_5%2Felectric_machine_design%3Atransformer-core-material-requirements) — Electric Machine Design, chapter 1