Search

Premium Membership ♕

Limited Time Offer: Save 15% on PRO Plan with discount code: LRN15 and study specialized LV/MV/HV technical articles and studies.

Home / Download Center / Electrical Engineering Books and Technical Guides / Electrical engineering guides / Electricity and magnetism textbook with exercises – Physics matters!

Definition of the magnetic field

Since magnetic monopoles don’t seem to exist, it would not make much sense to define a magnetic field in terms of the force on a test monopole. Instead, we follow the philosophy of the alternative definition of the electric field, and define the field in terms of the torque on a magnetic test dipole.

Electricity and magnetism textbook for you - Physics matters!
Electricity and magnetism textbook for you – Physics matters!

This is exactly what a magnetic compass does: the needle is a little iron magnet which acts like a magnetic dipole and shows us the direction of the earth’s magnetic field.

d / A - from a square loop of wire short- ing across a battery. It acts very much like a bar magnet, but its strength is more easily quantified.
d / A – from a square loop of wire short- ing across a battery. It acts very much like a bar magnet, but its strength is more easily quantified.

To define the strength of a magnetic field, however, we need some way of defining the strength of a test dipole, i.e., we need a definition of the magnetic dipole moment. We could use an iron permanent magnet constructed according to certain specifications, but such an object is really an extremely complex system consisting of many iron atoms, only some of which are aligned.

A more fundamental standard dipole is a square current loop. This could be little resistive circuit consisting of a square of wire shorting across a battery.

We will find that such a loop, when placed in a magnetic field, experiences a torque that tends to align plane so that its face points in a certain direction. (Since the loop is symmetric, it doesn’t care if we rotate it like a wheel without changing the plane in which it lies).

It is this preferred facing direction that we will end up defining as the direction of the magnetic field.

e / A - self to the surrounding magnetic field
e / A – self to the surrounding magnetic field

Experiments show if the loop is out of alignment with the field, the torque on it is proportional to the amount of current, and also to the interior area of the loop. The proportionality to current makes sense, since magnetic forces are interactions between moving charges, and current is a measure of the motion of charge.

The proportionality to the loop’s area is also not hard to understand, because increasing the length of the sides of the square increases both the amount of charge contained in this circular “river” and the amount of leverage supplied for making torque.

Two separate physical reasons for a proportionality to length result in an overall proportionality to length squared, which is the same as the area of the loop. For these reasons, we define the magnetic dipole moment of a square current loop as:

Dm = IA
[definition of the magnetic dipole moment of a square current loop]

We now define the magnetic field in a manner entirely analogous to the second definition of the electric field:

The magnetic field vector, B, at any location in space is defined by observing the torque exerted on a magnetic test dipole Dmt consisting of a square current loop. The field’s magnitude is |B| = τ/Dmt sinθ, where θ is the angle by which the loop is misaligned.

The direction of the field is perpendicular to the loop; of the two perpendiculars, we choose the one such that if we look along it, the loop’s current is counterclockwise.

We find from this definition that the magnetic field has units of N · m/A · m2 = N/A · m. This unwieldy combination of units is abbreviated as the tesla, 1 T = 1 N/A·m. Refrain from memorizing the part about the counterclockwise direction at the end.

The nonexistence of magnetic monopoles means that unlike an electric field, h/1, a magnetic one, h/2, can never have sources or sinks. The magnetic field vectors lead in paths that loop back on themselves, without ever converging or diverging at a point.

Title:Electricity and magnetism textbook  – Benjamin Crowell
Format:PDF
Size:11.2 MB
Pages:218
Download:Right here | Video Courses | Membership | Download Updates
Electricity and magnetism textbook for you – Physics matters!
Electricity and magnetism textbook for you – Physics matters!

Premium Membership

Get access to premium HV/MV/LV technical articles, advanced electrical engineering guides, papers, and much more! It will help you to shape up your technical skills in your everyday life as an electrical engineer.
50% Discount 💥 - Save 50% on all 90+ video courses with Enterprise Membership plan.

More Information

3 Comments


  1. Andi Faharuddin
    Jul 09, 2022

    This website is really useful mainly for whom are engaged in the field of electrical engineering. Besides, the website is both deeply and comprehensively enough in terms of practical data. In several cases, I use it as a reference. Keep going.


  2. Jean de Dieu UWAJENEZA
    Feb 23, 2021

    Thx if we want I need the exercise s of electricity and magnetism.


  3. Alimamy s bundu
    Aug 19, 2020

    I want to become an electrical engineer in the future

Leave a Reply to Alimamy s bundu

Tell us what you're thinking. We care about your opinion! Please keep in mind that comments are moderated and rel="nofollow" is in use. So, please do not use a spammy keyword or a domain as your name, or it will be deleted. Let's have a professional and meaningful conversation instead. Thanks for dropping by!

  ×  six  =  eighteen

Learn How to Design Power Systems

Learn to design LV/MV/HV power systems through professional video courses. Lifetime access. Enjoy learning!

Subscribe to Weekly Newsletter

Subscribe to our Weekly Digest newsletter and receive free updates on new technical articles, video courses and guides (PDF).
EEP Academy Courses - A hand crafted cutting-edge electrical engineering knowledge