# 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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