Electric fields, magnetic fields and Lorentz frames

In summary, the conversation discusses the process of proving that if E and B are perpendicular in one Lorentz frame, they are perpendicular in all Lorentz frames. The method involves contracting the tensor F with its dual, which shows that E.B is a Lorentz invariant. The conversation also mentions the steps to follow, such as finding the dual tensor and forming a scalar. It is suggested to refer back to the textbook for more information.
  • #1
golfingboy07
17
0
Not sure how to go about proving that if E and B are perpendicular in one Lorentz frame they are perpendicular in all Lorentz frames.
 
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  • #2
Contract the tensor F with its dual. This will show that E.B is a Lorentz invariant.
 
  • #3
ok. would you be able to start me off though?
 
  • #4
Do you know the tensor F in terms of E and B?
If you don't know that much, you can't start the problem.
Go back to the textbook.
 
  • #5
yes i know what the F tensor is in terms of the components of E and B
 
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  • #6
Find the dual tensor
{\cal F}_{\mu\nu}=\epsilon_{\mu\nu\rho\sigma}F^{\rho\sigma}.
Then form the scalar
{\cal F}_{\mu\nu}F^{\mu\nu}.
This will be proportional to {\bf E\cdot B}.
My latex didn't work, so try to read the above. Sorry.
 
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Related to Electric fields, magnetic fields and Lorentz frames

1. What is an electric field?

An electric field is a region of space that exerts a force on electrically charged objects. It is created by electric charges and can be either positive or negative. The strength of an electric field is measured in units of volts per meter (V/m).

2. What is a magnetic field?

A magnetic field is a region of space that exerts a force on magnetically charged objects. It is created by moving electric charges and can be either north or south. The strength of a magnetic field is measured in units of tesla (T).

3. What is the relationship between electric and magnetic fields?

Electric and magnetic fields are closely related and interact with each other. When an electric field changes, it creates a magnetic field, and vice versa. This phenomenon is known as electromagnetic induction and is the basis for many modern technologies.

4. What is a Lorentz frame?

A Lorentz frame, also known as a reference frame, is a coordinate system used to describe the position and motion of objects in space and time. It is based on the principles of relativity and is used in physics to study the effects of special relativity on objects moving at high speeds.

5. How do electric and magnetic fields change in different Lorentz frames?

In different reference frames, electric and magnetic fields can appear to be different due to the effects of relativity. Specifically, the strength and direction of the fields can change depending on the relative motion between the observer and the charged object. However, the laws of electrodynamics hold true in all inertial reference frames.

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