A cosmic ray proton impinges on the Earth near the equator with a vertical velocity of . We may assume that the horizontal component of the Earth’s magnetic field at the equator is . We have to calculate the ratio of the magnetic force on the proton to the gravitational force on it.

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Mass of the proton,

Charge of the proton,

Velocity of the proton,

and the Earth’s magnetic field at the equator,

At the equator the Earth’s magnetic field in the north-south direction and as the proton is coming down vertically, the velocity vector of the proton and the Earth’s magnetic field vector will be orthogonal. Magnetic force on proton will be

where is the unit vector in the east-west direction.

Therefore,

The gravitational force on the proton will be