Geometric transformation of E field to B ?

In summary, when an electric charge is stationary, it generates an electric field with zero curl. When it moves, it generates a circulating magnetic field. This change, called a transformation, is described by Maxwell's equations.
  • #1
Ghost117
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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?
 
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  • #2
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
 
  • #3
Ghost117 said:
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/ .
 
  • #4
bcrowell said:
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.
 
  • #5
According to numerous posts on PF, Griffiths does cover this topic in a manner similar to Purcell.
 
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  • #6
marcusl said:
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.
 
  • #7
Ghost117 said:
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.
 

1. How does a geometric transformation convert an electric field to a magnetic field?

A geometric transformation involves changing the reference frame or orientation of an electromagnetic field. In the case of converting an electric field to a magnetic field, this transformation involves changing the direction of the electric field to create a perpendicular magnetic field.

2. Can a geometric transformation change the magnitude of an electric field?

No, a geometric transformation does not change the magnitude of an electric field. It only changes the direction of the field, which in turn creates a new magnetic field.

3. What types of geometric transformations can be used to convert an electric field to a magnetic field?

There are various types of geometric transformations that can be used, such as rotation, reflection, and translation. However, the specific type of transformation used will depend on the orientation and direction of the initial electric field.

4. How is the strength of the resulting magnetic field determined in a geometric transformation?

The strength of the resulting magnetic field is determined by the strength of the initial electric field and the angle at which the transformation is applied. The stronger the initial electric field and the greater the angle of transformation, the stronger the resulting magnetic field will be.

5. What are some practical applications of geometric transformations in converting E field to B field?

Geometric transformations are used in various devices and technologies involving electromagnetic fields, such as antennas, motors, and generators. They are also essential in understanding the behavior of electromagnetic waves in different reference frames and media.

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