The Tevatron accelerator at Fermilab (Illinois) is designed to carry an 11 mA beam of protons traveling at very nearly the speed of light (3

Question

The Tevatron accelerator at Fermilab (Illinois) is designed to carry an 11 mA beam of protons traveling at very nearly the speed of light (300,000,000 m/s) around a ring 6300 m in circumference. How many protons are stored in the beam

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Thu Cúc 4 years 2021-07-20T13:19:51+00:00 1 Answers 38 views 0

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  1. thachthao
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    2021-07-20T13:21:26+00:00
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    Answer:

    The number  is  N= 1.442*10^{12} \ protons

    Explanation:

    From then question we are told that

       The current carried is I_p = 11mA =11 *10^{-3}A

        The speed is c = 3.0*10^8 m/s

        The circumference is D = 6300 \ m

    Mathematically current is expressed as

                     I = \frac{Q}{t} where Q is the quantity of charge passing through a conductor and t is the time in seconds

     The time t can be mathematically represented as

                     t = \frac{D}{ c}

    Substituting this into the equation fro current

                     I = \frac{Q}{\frac{D}{c} }

    Now making the quantity of charge the subject of the formula

                Q = \frac{I * D}{c}

    Generally the number of proton in the beam is mathematically represented as  

                N = \frac{Q}{n}

    Where n is the charge on one proton with a value of n= 1.602*10^{-19}C

    Now substituting for q in the equation for N

                 N = \frac{I * D}{c * n}

    Substituting values

                N = \frac{11*10^{-3} * 6300}{ 3.0*10^8 * 1.602 *10^{-19}}

                    N= 1.442*10^{12} \ protons

         

         

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