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Measuring the Charge to Mass Ratio of Particles
One way to measure the charge to mass ratio of particles is to send them through a region of space in which there are both electric and magnetic fields.
The fields must be (as near as possible) uniform.
The fields are oriented such that the force due to the electric field, FE is in the same direction but opposite sense to the force due to the magnetic field, FM
This means that the two fields must be at 90 to each other as shown here.
If the particles pass though the fields undeflected, then the two forces must have equal magnitudes. 
The diagram above assumes that the charge, q is a positive charge.
 
The force due to the electric field is independent of the velocity of the particles.
The force due to the magnetic field depends on the velocity of the particles.
Therefore, for a given pair of field strengths, E and B, the two forces can only be equal for one velocity.
 
We can know the speed of the particles if we know the potential difference, V through which they are accelerated.
During acceleration, electrical potential energy is converted to kinetic energy.
So we can write
therefore
in which we see the charge to mass ratio, q/m of the particles.
 
The force due to the magnetic field is given by
 
where v is the velocity and B is the magnetic flux density.
 
The force due to the electric field is given by 
 
where E is the electric field strength.
 
If these two forces have equal magnitude then the velocity of the particles is given by 
 
Therefore, if we find that the particles pass undeflected though the fields 
 
and so the charge to mass ratio can be found using 
 
in which E is electric field strength, B is magnetic flux density and V is the potential difference through which the particles were accelerated to send them into the fields.
 
See also Measuring the Charge to Mass Ratio of Electrons
 
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