Question

Two protons are aimed directly toward each other by a cyclotron accelerator with speeds of 1200 km/s , measured relative to the earth. Find the maximum electrical force that these protons will exert on each other?

Answer 1

The maximum electrical force is
`2.512*10^(-2)\ N`.

Step-by-step explanation:

Given that,

Speed of cyclotron = 1200 km/s

Initially the two protons are having kinetic energy given by

`(1)/(2)mv^2=(1)/(2)mv^2`

When they come to the closest distance the total kinetic energy is converts into potential energy given by

Using conservation of energy

`mv^2=(kq^2)/(r)`

`r=(kq^2)/(mv^2)`

Put the value into the formula

`r=(8.99*10^(9)*(1.6*10^(-19))^2)/(1.67*10^(-27)*(1200*10^(3))^2)`

`r=9.57*10^(-14)\ m`

We need to calculate the maximum electrical force

Using formula of force

`F=(kq^2)/(r^2)`

`F=(8.99*10^(9)*(1.6*10^(-19))^2)/((9.57*10^(-14))^2)`

`F=2.512*10^(-2)\ N`

Hence, The maximum electrical force is
`2.512*10^(-2)\ N`.