Question

A singly ionized particle (charge =+e) beam of various isotopes moving at various speeds through a region of electric and magnetic fields ,with E V m =1000 / and B T = 0.5 . a) what should be the angle between these crossed fields so that they act like a velocity selector? Draw a picture indicating field directions. b) Explain clearly how this setup selects a single velocity among many within the beam. c) Calculate the value of this selected speed. d) Draw another diagram showing how you would separate the various isotopes (i.e. describe mass spectrometer)

Answer 1

a) angle between E and B should be 90⁰ to use it as a velocity selector.

+ + + + XXXXXXB x x x x x x 1 xx x x x

The magnetic field is into the plane and electric field is vertically downwards.

b) The electric force acting on a charged particle moving through an electric field in perpendicular direction is given by

Fe = qE .

Similiarly the Lorentz force acting on it is given by

Fb = q ( v×B) = qvB since v and B are perpendicular.

When Fe = Fb the charge passes through the region of the mutually perpendicular electric and magnetic fields without any deviation.

Then V = E/B .

That means , only those with this particular velocity will pass through it without any deflection.

Hence acts as a velocity selector.

c) given E = 1000 Vm

B = 0.5 T

V = E/B = 1000/.5 = 2000 m/s

d)

к xxxxx - - - - - - - - - В х у

In mass spectrometer after passing through the velocity selector, the beam is passed through a region of magnetic field alone.

The charged particle will take a circular path and centripetal force is provided by the Lorentz force.

Hence MV²/ R = qVB

Where M - Mass of the isotope/charge

R - radius of the circular path.

From the above equation

R = VM / Bq

Substituting for V

R = EM / qB² .

Thus depending on mass of the isotope , it execute the circular path with a specific radius. Hence isotopes can be separated or we get a spectrum of various isotopes.