Possible Error in Vector Calculus Book

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There is a section that contains dealings with Maxwell's equations in my vector calc book, and there are, to my belief, numerous errors. Some of them I am certain on, but the is one I am not so sure on, although it would be a bigger blunder.

The book describes Maxwell's equations as, having E as electric field and H magnetic field:
[tex]\nabla[/tex][tex]\cdot[/tex]E=[tex]\rho[/tex]
[tex]\nabla[/tex][tex]\cdot[/tex]H=0
[tex]\nabla[/tex][tex]\times[/tex]E+[tex]\partial[/tex]B/[tex]\partial[/tex]t=0
[tex]\nabla[/tex][tex]\times[/tex]H-[tex]\partial[/tex]D/[tex]\partial[/tex]t=J

Aside from current density J not being bold due to being a vector, from what I know if one wishes to write maxwell's equations without using constants, they must be written:
[tex]\nabla[/tex][tex]\cdot[/tex]D=[tex]\rho[/tex]
[tex]\nabla[/tex][tex]\cdot[/tex]B=0
[tex]\nabla[/tex][tex]\times[/tex]E+[tex]\partial[/tex]B/[tex]\partial[/tex]t=0
[tex]\nabla[/tex][tex]\times[/tex]H-[tex]\partial[/tex]D/[tex]\partial[/tex]t=J

Second, they defined H as magnetic field, when it is magnetization. Is there something wrong here?
 

Answers and Replies

  • #2
pam
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It would help if you named the book and author thereof.
The book is probably using "Heaviside units", which are rationalized without the
epsilonzero and muzero. You should use \cdot to get the divergence right.
You are right about the D and B in the first two equations.
The names given to B and H vary widely among different books.
Some books call H "magnetic field", others call B "magnetic field".
I prefer the term for B, which is the physical magnetic equivalent of E.
The names used for B are even more varied and confusing.
"Magnetization" is always used for the magnetic moment per unit volume
(to within varying factors of 4 pi). In your units, it would equal M=B-H.
Your book probably just wants to demonstrate the math, and doesn't care much about the physics.
 
  • #3
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Sorry about the LaTex, it's the first time I've ever used it. I had the /cdot in before, but I must've deleted it while trying to make it look better.
The book is Vector Calculus (5th Edition) by Jerrold E. Marsden and Anthony J. Tromba.
Actually, I just noticed, the dot is there at the upper right corner of the del, but I DID have it look like a divergence before as aforementioned.
 
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  • #4
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In a lab setting, physicists deals with the H field and the E field. This is because we use currents to create a magnetic field, and H is what we control directly. That is, B is dependent on H, but we can always directly control H. However, we use potentials to create an electric field directly.
 

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