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 68.0 m in diameter and has a 0.37 A beam, how many electrons are in the beam

Answer 1

The no. of electron in the beam =
`1.64*10^(12)`

Step-by-step explanation:

Given :

The diameter of circular ring = 68 m.

The current flowing in the beam = 0.37 A

Speed of light =
`3*10^(8) ms^(-1)`

We know that the current is equal to the charge per unit time.

⇒
`I = (Q)/(t)`

∴
`Q=It`

Here given in the question, electron revolving in a circle with the diameter

`d = 68`m

⇒ Time take to complete one round
`(t) =`
`(\pi d )/(v)`

∴
`Q = (I\pi d )/(v)`

`Q = (0.37 * 3.14 * 68)/(3 * 10^(8) )`

`Q = 26.33 * 10^(-8)`

Now, for finding the no. of electron we have to divide
`Q` to the charge of the electron
`q = 1.6 * 10^(-19)`

∴
`n` =
`(26.33 * 10^(-8) )/(1.6 * 10^(-19) )`

`n = 1.64 * 10^(12)`

Thus, the no. of electron in the beam is
`1.64 * 10^(12)`.