I asked on Twitter the other day

What is the historical reason for denoting magnetic filed “B”?

Eric Eekhoff sent me an answer and with his permission I’m copying his email below:

Hi John,

I saw your question on your GrokEM twitter account about why magnetic field was denoted as

B. I recall that Maxwell just used the lettersAthroughHfor vectors in his Treatise on Electricity and Magnetism and some of them stuck and some of them didn’t.Ais still used for vector potential,Bfor magnetic field (or magnetic induction or flux density, depending who you ask),Hfor magnetic intensity, etc. Maxwell usedCandGfor other vectors that I don’t recall at the moment. They, for some reason, never stuck.Hope that helps. Have a good day,

Eric

tldr version: historical accident. Like so many other things.

It is my understanding that Maxwell’s equations as they are known today are largely due to Heaviside. Maxwell’s original equations were more numerous and redundant. Heaviside understood them, saw the redundancy, and simplified them into the form we are familiar with today. I suspect that some of the original fields/vectors went away during this process.

Jim: I believe you’re right. I have run across a couple references saying that his original statement had 20 equations. Four vector-valued equations would expand to 12 scalar equations, so vector notation alone does not explain why we have four equations and he had 20. There must have been some redundancy, as you said. And the Wikipedia article on Heaviside does give the credit for this simplification to Heaviside.

I did a little more research and I found an article by Ralph Baierlein in the American Journal of Physics, Vol. 68, No. 8, p. 691, August 2000. He writes “The symbols A, B, and H denote three prominent vector fields in electromagnetism. The choice of those three letters appears to be an alphabetical accident of history.” Baierlein gives some good commentary on why Maxwell may have chosen the symbols he did … “With good classical sense and unwitting foresight about its role in quantum theory, Maxwell gave the vector potential precedence over the magnetic (induction) field and assigned it the letter A.”

The paper mentioned by Eric E is available at : http://dx.doi.org/10.1119/1.19524

Both E and B can be derived from A and phi (http://en.wikipedia.org/wiki/Electric_field). The electric field also has D and E which describe it, similar to H and B.

M is used to indicate magnetization(http://en.wikipedia.org/wiki/Magnetic_field).

Reitz, Milford and Christy is the undergraduate book which most students from my era used. I recommend it. You can get a copy from abe.com for $4. + shipping.

(By the way, it’d be great if there were an html tag for your blog that permitted texxing…

w0w!thanks for the eye the reminder. now i remember Maxwell using letters A through H for vectors. And yes it Was Heaviside who made the simplification but Maxwell also did shared the idea, this was a good discussion to prove Maxwell, as helpful as johnson law group.

w0w!thanks for the eye the reminder. now i remember Maxwell using letters A through H for vectors. And yes it Was Heaviside who made the simplification but Maxwell also did shared the idea, this was a good discussion to prove Maxwell, as helpful as johnson law group.

Maxwell’s symbols (here), with modern translation behind the symbols (symbol + name), were:

A A vector potential

B B magnetic field B

C I total current (through a cross section)

D D electric displacement field

E E electric field

F f force density (f = ρE + JxB)

G v velocity in a point

H H magnetic field H

I M magnetization M

J J current density

I’d say and read here ( http://answers.yahoo.com/question/index?qid=20100721225709AAX19tQ ) that the letter B for magnetic field was chosen because the earths magnetic field always turns a compass towards the north (the boreal hemisphere).

boreal –> letter B

at least it makes some sense to me.

Actually, B is to represent the bi-polar field as the magnetic field is always bi-polar. As of date, mono-polar magnet doesn’t exist. So, the term “B” means the bi-polar field intensity (density).