Question Regarding Electromagnetic Fields in Special Relativity

In summary, the Biot-Savart Law states that the equation for the magnetic field around a charged particle moving with constant velocity is given by B= (1/c^2) * v X E. However, the relativistic description for the magnetic field, where B and E are the nonrelativistic magnetic and electric fields, is given by B'= gamma * (B - (1/c^2) * v X E) - ((gamma-1)/v^2) * (B * v) * v. This means that B' is always 0 if the velocities in the two equations are equal. However, the first equation is only an approximation and the correct equations for E and B are the last two equations
  • #1
Savant13
85
1
According to the http://en.wikipedia.org/wiki/Biot-Savart_Law" [Broken], the equation for the magnetic field around a charged particle moving with constant velocity is

[tex]
\mathbf{B} = \frac{1}{c^2} \mathbf{v} \times \mathbf{E}
[/tex]

But then, http://en.wikipedia.org/wiki/Mathematical_descriptions_of_the_electromagnetic_field" [Broken], the relativistic description for the magnetic field, where B and E are the nonrelativistic magnetic and electric fields is

[tex]
\mathbf{B} ' = \gamma ( \mathbf{B} - \frac{1}{c^2} \mathbf{v} \times \mathbf{E})- \frac{\gamma - 1}{v^2} ( \mathbf{B} \cdot \mathbf{v} ) \mathbf{v}
[/tex]

But this would mean that B' is always 0. Am I misunderstanding something? Is one of these equations the wrong one to use?

Would the B in the relativistic equation be zero to begin with?
 
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  • #2
In the first equation v is velocity of the particle, while in the second one the same letter is used to mean relative velocity of reference frames. If these two velocities are equal then B' = 0 because the particle is at rest in the '-reference frame.
 
  • #3
Read carefully, the Wiki article on BS says
"Note that the law is only approximate," for the equation B= qvXr/r^3.
To put it more clearly, that equation is wrong.
The correct equations for E and B are the last two equations in that section.
They do include B=vXE, but E is the complicated field, not the NR Coulomb field.
The second equation you give is for a Lorentz transformation of the fields, and refers to different things than your first equation.
 

1. What is the relationship between electromagnetic fields and special relativity?

In special relativity, electromagnetic fields are considered to be two aspects of the same phenomenon. This is because special relativity unifies electric and magnetic fields into a single electromagnetic field, and the laws of electromagnetism are valid in all frames of reference within special relativity.

2. How does special relativity affect the behavior of electromagnetic fields?

Special relativity predicts that the strength of an electromagnetic field will vary depending on the observer's frame of reference. The speed of light is also considered to be the maximum velocity for any object, including electromagnetic waves, in special relativity.

3. Can special relativity explain the behavior of electromagnetic waves?

Yes, special relativity provides a framework for understanding the behavior of electromagnetic waves. It explains how the velocity of light is constant in all inertial frames of reference and how electromagnetic waves can have different frequencies and wavelengths in different frames of reference.

4. Are there any experiments that support the relationship between electromagnetic fields and special relativity?

Yes, there have been numerous experiments that support the predictions of special relativity, including the famous Michelson-Morley experiment. This experiment showed that the speed of light is the same in all directions, regardless of the observer's frame of reference.

5. How does special relativity impact our understanding of the electromagnetic spectrum?

Special relativity helps us understand that the electromagnetic spectrum is a continuous range of frequencies and wavelengths, and that these properties can be perceived differently depending on the observer's frame of reference. It also explains the relationship between the different types of electromagnetic waves, such as radio waves, light waves, and gamma rays.

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