---
title: "State Ampere's circuital law"
subject: "Electromagnetism"
chapter: 3
key: "semester_3/electromagnetism:ampere-law-statement-with-example"
source: https://www.bctengineer.com/q/semester_3/electromagnetism/ampere-law-statement-with-example
site: BCT Engineering
---

# State Ampere's circuital law

Electromagnetism · Chapter 3: Magnetic field

- Asked in: 2070 Chaitra, 1 marks; 2069 Chaitra, 3 marks (asked 2 times)
- Video: [Ampere's Circuit Law Explained: Magnetic Field Intensity Fundamentals](https://www.youtube.com/watch?v=oGjnGylALXw) — Engineering Funda
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_3/electromagnetism/ampere-law-statement-with-example
- Whole chapter: https://www.bctengineer.com/md/semester_3/electromagnetism/chapter-3

## Question

State Ampere's circuital law (with relevant examples).

## Short answer

Ampere's law: ∮ H·dl = I_enc. For an infinite straight wire, symmetry gives H = I/(2πρ) a_φ. The law also yields fields for coaxial cables, solenoids, and toroids.

## Answer

**Ampere's circuital law:** the line integral of the magnetic field intensity H around any closed path equals the net current enclosed by that path.

```text
∮ H·dl = I_enc          (point form: ∇×H = J)
```
The direction of the current and the direction of the path follow the right-hand rule. The law is used to find H for symmetrical current distributions by choosing a closed path (Amperian loop) on which H is constant and tangential.

#### Example: infinitely long straight wire carrying current I
Take a circle of radius ρ around the wire as the Amperian path. By symmetry H has only an a_φ component of constant value on the circle.

```text
∮ H·dl = H_φ (2πρ) = I
H = I/(2πρ)  a_φ     (A/m)
```

The same method gives the field of a coaxial cable, a solenoid (H = NI/l inside), and a toroid (H = NI/(2πρ)).

## Check yourself

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

1. Ampere's circuital law says ∮H·dl equals:
   A. Enclosed charge
   B. Net enclosed current
   C. Zero always
   D. Flux through the path
   Answer: B. ∮H·dl = I_enc. (Key point: Statement)

2. For an infinite wire, H at distance ρ is:
   A. I/(2πρ²)
   B. I/(2πρ) a_φ
   C. I/(4πρ)
   D. Iρ/2π
   Answer: B. H(2πρ) = I. (Key point: Straight wire)

3. A good Amperian loop is one on which H is:
   A. Zero
   B. Constant and tangential
   C. Random
   D. Perpendicular to the path
   Answer: B. Then H comes out of the integral. (Key point: Choice of path)

## Related in Electromagnetism

- [Ampere's law and boundary H components](https://www.bctengineer.com/question.md?key=semester_3%2Felectromagnetism%3Aamperes-law-surface-current-boundary) — Electromagnetism, chapter 3
- [Ampere's law vs continuity equation](https://www.bctengineer.com/question.md?key=semester_3%2Felectromagnetism%3Aampere-law-conflict-continuity) — Electromagnetism, chapter 3, asked 2×

## Related in other subjects

- [Ampere's law, field of straight wire](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Aampere-law-straight-wire-field) — Engineering Physics, chapter 8, asked 5×
- [Biot-Savart vs Ampere's law, coil axis](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Abiot-ampere-compare-coil-axis) — Engineering Physics, chapter 8
- [Ampere's law, Maxwell's modification](https://www.bctengineer.com/question.md?key=semester_1%2Fengineering_physics%3Aampere-law-maxwell-modification-displacement) — Engineering Physics, chapter 9