A magnetic field set up using Helmholtz coils (described in Question 16 above) is uniform in a small region and has a magnitude of `0*75T`. In the same region, a uniform electrostatic field is maintained in a direction normal to the common axis of the coils. A narrow beam of (single species) charged particles all accelerated through `15kV` enters this region in a direction perpendicular to both the axis of the coils and the electrostatic field. If the beam remains undeflected when the electrostatic field is `9xx10^5Vm^-1`, make a simple guess so to what the beam contains. Why is the answer not unique?

Explanation

For an undeflected particle (beam) of charge e and mass m, moving in an external electric field E and magnetic field B with a velocity v, we have :
`eE = evB`
`rArr" " v = E/B`
Here, `B = 0.75 T`
`E = 9 xx 10^(5) V m^(-1)`
` :. " " v = (9 xx 10^(5))/(0.75) m s^(-1) `
` = 12 xx 10^(6) m s^(-1) `
K.E. of the charged particle will be :
` = 1/2 mv^(2) = eV`
Where V is the voltage through the charged particle is accelerated
`rArr" " e/m = v^(2)/(2V) = (144 xx 10^(12))/(2 xx 15,000) `
` = 4.8 xx 10^(7) C kg^(-1)`
From the charge to mass ratio of the particle obtained above, the particle can be deuteron.
The answer is not unique because only the ratio of charge to mass is determined. Other possible answers are `He^(+ +), Li^(+ + +) `, etc.
` :. He^(+ +) " and " Li^(+ + + )` also have the same value of `e//m [:. e/m = (2e)/(2m) = (3e)/(3m)]`