A uniform magnetic field with a slit system as shown in Fig. is to be used as a momentum filter for highenergy charged particles. With a field B tesla, it is found than the filter transmits `alpha` each of energy 5.3MeV. The magnetic field is increased to 2.3 tesla and deuterons are passed into the filter. The energy of each deutrons are passed into the filter. The energy of each deutrons transmitted by the filter is ........... MeV.

Explanation

The positively charged particle enters the uniform magnetic field
at right angle. Therefore, the force acting on the charged particle
In the magnetic field acts as centripetal force.
`(mv^2)/(r)=qvBimplies mv=qrB`
`implies m^2v^2=q^2r^2B^2 implies p^2=q^2r^2B^2`
But `KE=(p^2)/(2m)`
`:. (KE)2m=q^2r^2B^2`
r is same for both particles.
`implies ((KE)_(alpha)2m_(alpha))/((KE)_(d)2m_(d))=(q_(alpha)^2r^2B^2)/(q_d^2r^2(2.3B)^2)`
`:. 5.3/((KE)_(d))xx4/2=4/1xx1/(2.3xx2.3)`
`implies (KE)_d=14.0185eV`