Question

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^(-5)Vm^-1`, make a simple guess so to what the beam contains. Why is the answer not unique?

Answer 1

Magnetic field, `B = 0.75 T`
Accelerating voltage, `V = 15 kV = 15 xx 10^(3)V`
Electrostatic field, `E = 9 xx 10^(5)Vm^(-1)`
Mass of the electron =m
Charge of the electron =e
Velocity of the electron = v
Kinetic energy of the electron `=eV`
`rArr (1)/(2)mv^(2)=eV`
`:. (e)/(m) = (v^(2))/(2V)` ...(1)
Since the particle remains undeflected by electric and magnetic fields, we can infer that the electric field is balancing the magnetic field.
`:. eE = evB`
`v = (E)/(B)` ...(2)
Putting equation (2) in equation (1), we get
`(e)/(m) = (1)/(2) (((E)/(B))^(2))/(V)=(E^(2))/(2VB^(2))`
`= ((9.0 xx 10^(5))^(2))/(2xx 1500 xx (0.75)^(2)) = 4.8 xx 10^(7)C//kg`
The value of specific charge e/m is equal to the value of deuteron or deuterium ions. This is not a unique answer. Other possible answers are `He^(++),Li^(+_`, etc.