Exploring the Relationship Between B and E

In summary, the permeability of free space refers to how much space itself is magnetized in the presence of a magnetic field. It is less than unity and can be thought of as a resistance, with a value of zero in ideal space. In Albert Shadowitz's The Electromagnetic Field, it is explained that the vectors E and B are analogous to each other, rather than E and H. However, the Lorentz force equation uses both E and B. Therefore, there is no clear counterpart for E and it remains uncertain whether it is analogous to B or H. As for the magnetic permeability of aluminum, its numerical value depends on the velocity and density, but more information is needed to determine an exact value.
  • #1
zeromodz
246
0
Since the permeability of free space is a measure of how free space resists a magnetic field, shouldn't it be inversely proportional like the permittivity of free space with respect to the electric field?

B = μqrsin / 4πr^2
E = q / 4πεr^2
 
Physics news on Phys.org
  • #2


The permeability of free space is NOT a measure of how free space resists a magnetic field.
 
  • #3


The permeability determines how much space itself is magnetized in the presence of a magnetic field. Since it is less than unity I think of it of like a resistance where the permeability equals zero in ideal space
 
  • #4


In Albert Shadowitz's The Electromagnetic Field, page 319-320, (you can find it at google.books http://books.google.com/books?id=31...resnum=2&ved=0CB4Q6AEwAQ#v=onepage&q&f=false") it's explained that

"When the theory of electricity and magnetism was first being developed it was believed that the vectors E and H were analogous to each other."

That made the constitutive equations D = epsilon E and B = mu H analogous.

But, "Today it is generally accepted that E and B are the analogous quantities, rather than E and H. For E is produced by any kind of charge, free or bound, just as B is caused by any kind of current, conventional or bound. D and H, on the other hand, are only produced by free charge and conventional current, respectively. From this point of view it is unfortunate that epsilon0 and mu0 were placed in opposite positions in the two defining equations."
 
Last edited by a moderator:
  • #5


shoestring said:
In Albert Shadowitz's The Electromagnetic Field, page 319-320, (you can find it at google.books http://books.google.com/books?id=31...resnum=2&ved=0CB4Q6AEwAQ#v=onepage&q&f=false") it's explained that

"When the theory of electricity and magnetism was first being developed it was believed that the vectors E and H were analogous to each other."

That made the constitutive equations D = epsilon E and B = mu H analogous.

But, "Today it is generally accepted that E and B are the analogous quantities, rather than E and H. For E is produced by any kind of charge, free or bound, just as B is caused by any kind of current, conventional or bound. D and H, on the other hand, are only produced by free charge and conventional current, respectively. From this point of view it is unfortunate that epsilon0 and mu0 were placed in opposite positions in the two defining equations."

E & H are analogous in 2 ways. First, E is in units of V/m, while H is in A/m. The ratio E/H is V/A or ohms. The E/H ratio of an e/m wave is the impedance of the medium. Also, E X H, the cross product, has units W/m^2. This is the radiated power per area, aka "Poynting Vector".

If we examine electric & magnetic fields in the boundary region between differing media, we get the following. The normal components of the B fields in the 2 media, Bn1 & Bn2, are equal. The normal components of the D fields in each medium are either equal or they differ by a mere constant, i.e. Dn1 - Dn2 = rho_s. The "rho_s" is the surface charge density. The B & D quantities behave in a similar fashion.

But the tangential fields at a boundary displays a different property. The tangential E field components are equal for materials 1 & 2, i.e. Et1 = Et2. Also, Ht1 = Ht2. So E & H behave analogously.

Based on the above, there is compelling reason to regard E & H as a pair, likewise w/ B & D. But hold on. The Lorentz force equation is as follows:

F = q*(E + (u X B)). Here, the Lorentz force is determined by E for the electric part, & B for magnetic. Hence a case can be made tying E to B.

So the conclusion is that there is no conclusion. Is E the counterpart of B or H? I don't think we have an answer.

Claude
 
Last edited by a moderator:
  • #6


I need some information of magnetic permeability of aluminium material,

its numerical value.
while my other velocities are in m/s, and density is kg/m^3
thanks
 

1. What is the relationship between B and E?

The relationship between B and E is a scientific concept that explores the correlation between two variables, B (independent variable) and E (dependent variable). This relationship can be positive, negative, or have no correlation at all.

2. How do scientists study the relationship between B and E?

Scientists use various methods to study the relationship between B and E. These methods include experiments, surveys, case studies, and observational studies. Each method offers its own advantages and limitations, and scientists must carefully choose the most appropriate method for their research question.

3. What factors can influence the relationship between B and E?

There are many factors that can influence the relationship between B and E. These factors can include external variables, such as environmental conditions or human behavior, as well as internal variables, such as biological processes or genetic factors. It is important for scientists to control for these factors in their research to accurately determine the relationship between B and E.

4. Is correlation the same as causation in the relationship between B and E?

No. Correlation refers to the strength and direction of the relationship between two variables, while causation refers to one variable directly causing a change in another. Just because B and E are correlated does not necessarily mean that one variable is causing the other. Other factors must be considered before determining causation in the relationship between B and E.

5. What are the real-world applications of studying the relationship between B and E?

Studying the relationship between B and E has many real-world applications. It can help scientists better understand the cause and effect of certain phenomena, inform public policies and interventions, and contribute to advancements in various fields, such as medicine and psychology. Additionally, understanding this relationship can help individuals make informed decisions about their health and well-being.

Similar threads

Replies
25
Views
1K
Replies
16
Views
1K
Replies
5
Views
844
  • Electromagnetism
Replies
5
Views
751
  • Electromagnetism
Replies
5
Views
1K
  • Electromagnetism
Replies
8
Views
889
  • Electromagnetism
Replies
4
Views
852
Replies
17
Views
1K
  • Electromagnetism
2
Replies
35
Views
3K
Replies
4
Views
1K
Back
Top