Question

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

Answer 1

Answer:

n = 3.1x10¹²

Explanation:

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

$I = \frac{q}{\Delta t} \rightarrow q = I*\Delta t$    (1)

Where:

I: is the electric current = 0.59 A

t: is the time

The time t is equal to:

$v = \frac{\Delta x}{\Delta t} \rightarrow \Delta t = \frac{\Delta x}{v}$   (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:

$\Delta x = 2\pi*r = \pi*d$     (3)

Where d is the diameter = 80.0 m

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

$q = I*\Delta t = I*\frac{\Delta x}{v} = \frac{I\pi d}{v} = \frac{0.59 A*\pi*80.0 m}{2.99 \cdot 10^{8} m/s} = 4.96 \cdot 10^{-7} C$      

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

$n = \frac{q}{e}$

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

$n = \frac{q}{e} = \frac{4.96 \cdot 10^{-7} C}{1.6 \cdot 10^{-19} C} = 3.1 \cdot 10^{12}$

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

I hope it helps you!