A beam of charged particle, having kinetic energy `10^3 eV`, contains masses `8xx10^(-27) kg and 1.6xx10^(-26) kg` emerge from the end of an accelerator tube. There is a plate at distance `10^2 m` from the end of the tube and placed perpendicular to the beam. Calculate the magnitude of the smallest magnetic field which can prevent the beam from striking the plate.

Explanation

Let `vecB` be required magnetic field and `E_k` the kinetic energy.
Maximum radius of circular path for the beam not to strike the plane
`r=(mv)/(qB)=(sqrt(2mE_k))/(qB) implies B=(sqrt(2mE_k))/(qr)`
Here `r=10^-2m` is same for both types of particles. For the particle of larger mass, B required will be more. This B will be minimum value required to prevent the beam from striking the plate.

`B_(min)=(sqrt(2xx1.6xx10^-26xx(10^3xx1.6xx10^-19)))/(1.6xx10^-19xx10^-2)`
`=(1.6sqrt2xx10^-21)/(1.6xx10^-21)=sqrt2T=1.414T`