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

Answer 1

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

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

                $N= 1.442*10^{12} \ protons$