MagnetismHard
Question
In a mass spectrometer used for measuring the masses of ions, the ions are initially accelerated by an electric potential V and then made to describe semicircular paths of radius R using a magnetic field B. If V and B are kept constant, ratio 
will be proportional to
will be proportional toOptions
A.
B.
C.R2
D.R
Solution
The centripetal force is provided by the magnetic force.
i.e.,
= qvB ....... (1)
where m = mass of the ion, v = velocity ,q = charge of ion, B = flux density of the magnetic field.
we have, v = Rω
or ω =
(from(1))
Energy of ion is given by,
E =
mv2 = m(Rω)2 = mR2 
or E =
....... (2)
If ions are accelerated by electric potential V, the energy attained by ions,
E = qV ....... (3)
from eqns(2)and(3)
qV =
or 
i.e.,
(If V and B are const.)
i.e.,
= qvB ....... (1)where m = mass of the ion, v = velocity ,q = charge of ion, B = flux density of the magnetic field.
we have, v = Rω
or ω =
(from(1))Energy of ion is given by,
E =
mv2 = m(Rω)2 = mR2 or E =
....... (2)If ions are accelerated by electric potential V, the energy attained by ions,
E = qV ....... (3)
from eqns(2)and(3)
qV =
or i.e.,
(If V and B are const.)Create a free account to view solution
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