Magnetic force between two parallel moving charges

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Discussion Overview

The discussion revolves around the magnetic force experienced between two parallel moving charges, particularly focusing on the conditions under which such forces arise and how they are perceived from different reference frames. Participants explore the implications of relativity on the interaction between the charges, considering both electric and magnetic forces in various contexts.

Discussion Character

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

Main Points Raised

  • One participant questions whether two charges moving parallel to each other with equal speed experience a magnetic force, suggesting that since they do not move relative to each other, they should not feel mutual magnetic influence.
  • Another participant emphasizes the need for a relativistic approach to determine the forces between moving charges, noting that both electric and magnetic forces are involved and that the situation is more complex than that of two wires carrying current.
  • A different viewpoint states that in the reference frame where the charges are at rest, they exert electrostatic forces on each other, while in a moving frame, both electric and magnetic forces act on them, related by the Lorentz transformation.
  • One participant clarifies that the perception of magnetic forces depends on the observer's frame of reference, asserting that moving charges can experience magnetic forces relative to a stationary observer.
  • Another participant discusses the relationship between electric and magnetic fields, suggesting that they are manifestations of the same underlying field, influenced by the relative motion of the observer and the charges.
  • A participant raises a related question about the behavior of highly relativistic charges, expressing confusion over the explanation that electric and magnetic forces cancel out, particularly in the frame of reference of the moving charges.
  • In response, another participant explains that while the electric repulsion weakens with distance, the resultant force in the lab frame is less than in the frame where the charges are at rest, but does not change from repulsive to attractive.

Areas of Agreement / Disagreement

Participants express differing views on the nature of forces between parallel moving charges, with some emphasizing the role of relativity and frame dependence, while others challenge the conventional explanations based on wire experiments. The discussion remains unresolved, with multiple competing perspectives presented.

Contextual Notes

Participants note that the definitions of force and the effects of motion on electric and magnetic fields are crucial to understanding the interactions, and that the complexity arises from the insistence on classifying forces as electric or magnetic.

  • #31
Exactly so. When psi = pi/2, i.e. in the transverse direction, (1 - beta^2 sin^2 psi)^3/2 becomes (1 - beta^2 )^3/2 = gamma^-3, so the transverse E in the lab frame is simply gamma times that in the rest frame of an electron. We can reach this result very simply by applying length contraction to a coin-shaped gaussian box with an electron at its centre.
 

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