Geometric transformation of E field to B ?

[Ghost117]

When a test charge is stationary, it generates an E field with zero curl.

When it moves, it generates a circulating magnetic field B...( as well as the E field.)

Is there a geometric reason for this? How does motion alone generate a circulating field B?

Can we call this change a 'transformation' even?

 

[DuckAmuck]

By moving an electric field, you are changing the electric field. A changing electric field is essentially a magnetic field.

Not sure how much calculus you know, but this is very well-understood. The relationship is described in Maxwell's equations.
https://en.wikipedia.org/wiki/Maxwell's_equations

 

[bcrowell]

Is there a geometric reason for this? How does motion alone generate a circulating field B?

The fundamental reason is relativity. The textbook by Purcell, Electricity and Magnetism, is the classic presentation of this. For a similar presentation, see section 23.2 of my book Light and Matter: http://lightandmatter.com/lm/ .

 

[Ghost117]

The fundamental reason is relativity. The textbook by Purcell, Electricity and Magnetism, is the classic presentation of this. For a similar presentation, see section 23.2 of my book Light and Matter: http://lightandmatter.com/lm/ .

Thanks much, that's what I needed i.e. a text that deals with this. I'm working through Griffiths E&M right now and I don't think he deals with it.

 

[marcusl]

According to numerous posts on PF, Griffiths does cover this topic in a manner similar to Purcell.

 

[Ghost117]

According to numerous posts on PF, Griffiths does cover this topic in a manner similar to Purcell.

It's not in chapter 5, maybe chapter 12 which introduces relativity.

 

[Ghost117]

It's not in chapter 5, maybe chapter 12 which introduces relativity.

p.s. By the way, it is in Griffiths chapter 12, pretty much the last section of the last chapter, has a section on the transformation from E to B. However, I think bcrowell was referring to purcell because that would deal with it in more depth.