Come Closer!

A Charged Particle of Mass \(m\) and Charge \(q\) is thrown with an initial velocity of \(v\) towards an infinite wire carrying a current \(i\) from an initial distance of \(d\).

If the minimum separation (in meters) between the particle and the wire, during the course of time, is \(\ell\), then Evaluate \(\ell\times 10^{49}\) to the nearest Integer

Details and Assumptions:

  • \(\mu_o = 4\pi \times 10^{-7}\frac{\text{N}}{\text{A}^2}\)
  • \(i = 5\text{ A}\)
  • \(m = 0.08\text{ g}\)
  • \(d = 4\text{ m}\)
  • \(v = 1.386\frac{\text{m}}{\text{s}}\)
  • \(q = 1\text{ C}\)

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