A charge partides round a 1 m radius circular particle accelerator at nearly the speed of light. Find : (a) The period (b) The centripetal acceleration of the charged particles

Respuesta :

Explanation:

It is given that,

Radius of circular particle accelerator, r = 1 m

The distance covered by the particle is equal to the circumference of the circular path, d = 2πr

d = 2π × 1 m

(a) The speed of satellite is given by total distance divided by total time taken as :

[tex]speed=\dfrac{distance}{time}[/tex]

Let t is the period of the particle.

[tex]t=\dfrac{d}{s}[/tex]

d = distance covered

s = speed of particle

It is given that the charged particle is moving nearly with the speed of light

[tex]t=\dfrac{d}{c}[/tex]

[tex]t=\dfrac{2\pi\times 1\ m}{3\times 10^8\ m/s}[/tex]

[tex]t=2.09\times 10^{-8}\ s[/tex]

(b) On the circular path, the centripetal acceleration is given by :

[tex]a=\dfrac{c^2}{r}[/tex]

[tex]a=\dfrac{(3\times 10^8\ m/s)^2}{1\ m}[/tex]

[tex]a=9\times 10^{16}\ m/s^2[/tex]

Hence, this is the required solution.