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2 years ago

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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

1 answer:

Lunna [17]2 years ago

3 0

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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