In Thomson's experiments with electron beams, when the magnetic force FM balanced the force of the electric field Fe, the veloci
1 answer:
In Thomson's experiment, when the magnetic force balanced the electric force, the velocity of the beam was
where E is the magnitude of the electric field and B the magnitude of the magnetic field.
Let's see why. The force exerted by the electric field of intensity E on each electron is
where
is the electron charge.
The force exerted by the magnetic field of intensity B on each electron is
where v is the speed of the electrons.
When the two forces are balanced, we have:
from which we find
where E is the magnitude of the electric field and B the magnitude of the magnetic field.
Let's see why. The force exerted by the electric field of intensity E on each electron is
where
The force exerted by the magnetic field of intensity B on each electron is
where v is the speed of the electrons.
When the two forces are balanced, we have:
from which we find
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We can solve the problem by using the law of conservation of energy:
- at the beginning, all mechanical energy of the object is just kinetic energy: , where m is the mass and v is the velocity
- at the point of maximum height, all mechanical energy of the object is just gravitational potential energy: , where h is the maximum height
Therefore, the conservation of energy becomes:
Re-arranging, we find the maximum height: