Magnetism as a Relativistic Phenomenon

In summary, the plus and minus on top of each other in the denominator can be factored out to get the final expression.
  • #1
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Consider a wire with charges moving with speed 'v'and '-v' in frame F (with charge q at distance s away moving at speed u).

In frame F', the charge q is stationary, and so the speeds of the charges in the wire are v+ and v-, where v- > v+

Hi guys, I have trouble following through the proof in step 12.81 and 12.82:

How did they get rid of the ± in the denominator? I tried using a2 - b2 = (a+b)(a-b) but it doesn't match the expression:

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  • #2
The plus and minus on top of each other are different solutions to the equation. Whether you choose to solve for positive or negative gamma in equation 12.81, the denominator comes out the same. Then, if you factor the denominator, you get the equation after 12.81.
 

1. What is the relationship between magnetism and relativity?

The relationship between magnetism and relativity is that magnetism is a relativistic phenomenon. This means that the behavior of magnets and electric currents can only be fully explained by taking into account the principles of relativity, particularly the theory of special relativity.

2. How does special relativity explain magnetism?

Special relativity explains magnetism by showing that the magnetic field is a result of the electric field in a moving reference frame. In other words, an electric current in motion creates a magnetic field due to the relativistic effects on the electric charges that make up the current.

3. Can magnetism exist without relativity?

No, magnetism cannot exist without relativity. The classical laws of electromagnetism, which do not take into account the principles of relativity, are not able to fully explain the behavior of magnetic fields. It is only through the principles of special relativity that magnetism can be fully understood.

4. How does magnetism affect time and space?

In special relativity, time and space are not absolute, but are relative to the observer's frame of reference. Magnetism can affect time and space because the presence of a magnetic field can alter the measurements of time and space for an observer in a different frame of reference.

5. What are some practical applications of magnetism as a relativistic phenomenon?

Some practical applications of magnetism as a relativistic phenomenon include particle accelerators, which use magnetic fields to accelerate charged particles to high speeds, and magnetic resonance imaging (MRI) technology, which uses strong magnetic fields to produce detailed images of the body's tissues and organs.

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