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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