A particle moving in magnetic and gravitational fields.

A charged particle of mass \(m=1\text{ kg}\) and charge \(q = 1\text{ C}\) is released from rest from a height \(H\) relative to the Earth's surface. A horizontal magnetic field of magnitude \(B = 1\text{ T}\) is applied. Find the minimum integral value of \(H\) in metres such that the particle never reaches Earth's surface.

Details and assumptions

  • The gravitational acceleration is constantly \(g = -9.8\text{ m/s}^2\).
  • There are no obstacles (e.g. a mountain, a building etc.) in particle's path.
  • Assume no other forces act on the particle except for magnetic and gravitational forces.

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