Electricity and Magnetism: The Surprise Connection

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Discussion Overview

The discussion revolves around the relationship between electric and magnetic forces in the context of moving charges. Participants explore how these forces interact and the implications of different reference frames on their magnitudes and effects. The conversation touches on theoretical aspects of electromagnetism, particularly in relation to Lorentz transformations and relativistic effects.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant posits that two like charges moving with the same velocity and perpendicular displacement should magnetically attract each other, raising questions about the existence of magnetic fields in different reference frames.
  • Another participant asserts that while the charges will repel in any frame, the magnitude of the repulsion differs, and both electric and magnetic fields are present in a moving frame, suggesting they are interrelated.
  • A participant references Lorentz transformations, implying their relevance to the discussion of electric and magnetic forces.
  • It is noted that the Coulomb repulsion generally exceeds magnetic attraction, except in cases of extremely relativistic velocities where the two forces may cancel out.
  • One participant shares a mathematical exploration of the ratio of magnetic force to electric force, concluding that it is inversely proportional to the square of the speed, indicating a very small value for typical speeds.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between electric and magnetic forces, particularly regarding their magnitudes in various reference frames. There is no consensus on the implications of these forces or their interactions, indicating ongoing debate.

Contextual Notes

Participants reference Lorentz transformations and relativistic effects without fully resolving the implications of these concepts. The discussion includes mathematical derivations that may depend on specific assumptions or definitions not fully articulated.

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You have two like charges with the same velocity and a displacement between them perpendicular to the velocity. Moving charges produce a magnetic field. The charges should magnetically attract one another.

Now consider the reference frame of the charges. There is no motion so no magnetic field exist. How is this possible?

The two charges exert a repulsive force on each other due to their electric field. How do these two forces relate to one another?

The answer (if you can figure it out) might surprise you.
 
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The charges will repel in either frame, just the magnitude of the repulsion will differ. In a moving frame, both a magnetic field and an electric field are present. The two fields are the same thing simply viewed through different frames.
 
So... Lorentz transformations much?
 
The Coulomb repulsion always exceeds the magnetic attraction, except when the velocities are extremely relativistic and the two forces cancel. In a Lorentz frame where the two particles are stationary, only the repulsive Coulomb force remains. See thumbnail derivation.

Bob S
 

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nice.

What I did is looked at the ratio of magnetic force to electric force. Most of the terms canceled each other an what I was left with is

FB/FE = v^2 * permeability of free space * the permeativity of free space

The only variable is time so I calculated the product of our constants, saw that it was a very small value. I knew from the equation that it is an inverse speed squared quantity because booth sides should be unit less ratios. Sure enough

FB/FE = v^2/c^2
 

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