Answer:
The number is [tex]N= 1.442*10^{12} \ protons[/tex]
Explanation:
From then question we are told that
The current carried is [tex]I_p = 11mA =11 *10^{-3}A[/tex]
The speed is [tex]c = 3.0*10^8 m/s[/tex]
The circumference is [tex]D = 6300 \ m[/tex]
Mathematically current is expressed as
[tex]I = \frac{Q}{t}[/tex] 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
[tex]t = \frac{D}{ c}[/tex]
Substituting this into the equation fro current
[tex]I = \frac{Q}{\frac{D}{c} }[/tex]
Now making the quantity of charge the subject of the formula
[tex]Q = \frac{I * D}{c}[/tex]
Generally the number of proton in the beam is mathematically represented as
[tex]N = \frac{Q}{n}[/tex]
Where n is the charge on one proton with a value of [tex]n= 1.602*10^{-19}C[/tex]
Now substituting for q in the equation for N
[tex]N = \frac{I * D}{c * n}[/tex]
Substituting values
[tex]N = \frac{11*10^{-3} * 6300}{ 3.0*10^8 * 1.602 *10^{-19}}[/tex]
[tex]N= 1.442*10^{12} \ protons[/tex]
