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

The number is
`N= 1.442*10^(12) \ protons`

Step-by-step 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 = (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 = (D)/( c)`

Substituting this into the equation fro current

`I = (Q)/((D)/(c) )`

Now making the quantity of charge the subject of the formula

`Q = (I * D)/(c)`

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

`N = (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 = (I * D)/(c * n)`

Substituting values

`N = (11*10^(-3) * 6300)/( 3.0*10^8 * 1.602 *10^(-19))`

`N= 1.442*10^(12) \ protons`