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Ratio Fb & Fg.doc

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Rajput AbdulWaheed Bhatti
Rajput AbdulWaheed Bhatti

The document describes calculating the ratio of the magnetic force to the gravitational force on a proton moving vertically at the Earth's equator. It gives the proton's speed, the horizontal component of Earth's magnetic field, the proton's mass, and the gravitational acceleration. It then shows the calculations of the magnetic force using the magnetic field and speed, and the gravitational force using mass and gravitational acceleration. The ratio of magnetic to gravitational force is calculated to be approximately 16.

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1 5 6 A cosmic-ray proton approaches Earth vertically at the equator, where the horizontal component of Earth¡¯s magnetic field is 3.5 10 T. If the proton is moving at 3.0 10 m/s, what is the ratio of the m ? ? ? agnetic force to the gravitational force on the proton? Solution MAGNETIC FORCE ON A MOVING CHARGED PARTICLE
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3 Let be the Magnetic Force & be the Gravitational Force, then (1) (2) where is the mass of the Proton B G B G p p F F F quB F m g m ? ? ? ? ? ? ? ? 19 6 5 27 2 18 9 27 2 9 2 Now, (1.6 10 ) (3.0 10 ) (3.5 10 ) (1.67 10 )(9.8 ) 16.8 10 . . . . 1.03 10 . 16.37 10 1.03 10 . . . . . ( 1) . . . . B G m X C X X X s F X T m F X kg s m X C T C T s s X kg m kg X s X C T s C kg s C A s kg A s kg A s A s ? ? ? ? ? ? ? ? ? ? ? ? ?

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Ratio Fb & Fg.doc

  • 1. 1 5 6 A cosmic-ray proton approaches Earth vertically at the equator, where the horizontal component of Earth¡¯s magnetic field is 3.5 10 T. If the proton is moving at 3.0 10 m/s, what is the ratio of the m ? ? ? agnetic force to the gravitational force on the proton? Solution MAGNETIC FORCE ON A MOVING CHARGED PARTICLE
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  • 3. 3 Let be the Magnetic Force & be the Gravitational Force, then (1) (2) where is the mass of the Proton B G B G p p F F F quB F m g m ? ? ? ? ? ? ? ? 19 6 5 27 2 18 9 27 2 9 2 Now, (1.6 10 ) (3.0 10 ) (3.5 10 ) (1.67 10 )(9.8 ) 16.8 10 . . . . 1.03 10 . 16.37 10 1.03 10 . . . . . ( 1) . . . . B G m X C X X X s F X T m F X kg s m X C T C T s s X kg m kg X s X C T s C kg s C A s kg A s kg A s A s ? ? ? ? ? ? ? ? ? ? ? ? ?