A particle moving in magnetic and gravitational fields.

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

Details and assumptions

  • The gravitational acceleration is constantly g=9.8 m/s2g = -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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