SPEAR is a storage ring at the Stanford Linear Accelerator which has a circulating beam of electrons that are moving at nearly the speed of light (2.998 108 m/s). If a similar ring is about 80.0 m in diameter and has a 0.59 A beam, how many electrons are in the beam

n = 3.1x10¹²

Explanation:

To find the number of electrons we need to find first the charge (q):

   (1)

Where:

I: is the electric current = 0.59 A

t: is the time

The time t is equal to:

  (2)

Where:

x: is the displacement

v: is the average speed = 2.998x10⁸ m/s

The displacement is equal to the perimeter of the circumference:

    (3)

Where d is the diameter = 80.0 m

By entering equations (2) and (3) into (1) we have:

Now, the number of electrons (n) is given by:

Where e is the electron's charge = 1.6x10⁻¹⁹ C  

Therefore, the number of electrons in the beam is 3.1x10¹².

I hope it helps you!