What is the formula for magnetic field when v is close to c?

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Discussion Overview

The discussion revolves around the formula for the magnetic field produced by a moving charge, particularly when the velocity of the charge approaches the speed of light (c). Participants explore the limitations of classical formulas and seek alternatives applicable in relativistic contexts.

Discussion Character

  • Exploratory, Technical explanation, Debate/contested

Main Points Raised

  • One participant suggests using the formula B = \frac{\mu}{4\pi} \frac{q[vr]}{r^3} for cases where v is much less than c, but questions its validity as v approaches c.
  • Another participant seeks clarification on whether the discussion pertains to the magnetic field generated by a single moving charge.
  • A reference to a specific equation from a lecture on electromagnetic theory is provided, indicating a potential alternative approach for relativistic speeds.

Areas of Agreement / Disagreement

Participants do not reach a consensus on the appropriate formula for the magnetic field when v is close to c, and multiple viewpoints regarding the applicability of different equations remain present.

Contextual Notes

The discussion highlights the need for a formula that accounts for relativistic effects, but does not resolve the specific mathematical steps or assumptions required for such a formula.

IPhO' 2008
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We can use B = [tex]\frac{\mu}{4\pi}[/tex] [tex]\frac{q[vr]}{r<sup>3</sup>}[/tex]
when v << c (c is a speed of light) but if v is nearly to c we can't use this formula.
What is a formula when v is nearly to c.
 
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