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 92.0 m in diameter and has a 0.40 A beam, how many electrons are in the beam

Answer 1

Answer:

$2.4\times 10^{12}$

Explanation:

We are given that

Speed of light,v=$2.998\times 10^8 m/s$

Diameter of ring,d=92 m

Radius,r=$\frac{d}{2}=\frac{92}{2}=46 m$

Current, I=0.40 A

We have to find the number of electrons in the beam.

We know that

Current,I=$\frac{q}{t}$

Where q= ne

$e=1.6\times 10^{-19} C$

Using the formula

$0.40=\frac{1.6\times 10^{-19}n}{\frac{2\pi r}{v}}$

$0.40=\frac{1.6\times 10^{-19}n\times v}{2\pi r}$

$0.40=\frac{1.6\times 10^{-19}n\times 2.998\times 10^8}{2\pi\times 46}$

$n=\frac{0.40\times 2\pi\times 46}{1.6\times 10^{-19}\times 2.998\times 10^8}=2.4\times 10^{12}$