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Q.NO
CBSE;Class XII;Physics;Moving Charges and Magnetism;Motion Of A
Charged Particle In An External Magnetic Field
Question
Solution
Consider a uniform magnetic field of strength B. Let a charged
particle of charge q be projected into the magnetic field with a
velocity v perpendicular to the direction of the magnetic field.
When the charged particle is moving perpendicular to the
magnetic field, the charged particle experiences maximum force
and this force is acting perpendicular to both the magnetic field
and velocity of the charged particle.
In the case of a charged particle in a magnetic field, the magnetic
force is acting perpendicular to the direction of velocity, and
thus the work done on the charged particle is zero. As the work
done on the charged particle is zero, there is no change in the
kinetic energy of the charged particle and the magnitude of the
velocity of the charged particle remains constant.
As the magnetic
force acting on the
charged particle is
perpendicular to
both the direction
of its velocity and
magnetic field, the
charged particle
moves in a circular
path and the
magnetic force acts
as centripetal force.
From the expression, it is clear that the time period of revolution
of the charged particle is independent of its speed.
Now, consider that the charged particle is projected at an angle,
theta, to the uniform magnetic field, which is anything other
than 90 degrees. It can be shown that the charged particle has a
velocity in the direction of the magnetic field and also in a
circular path, whose plane is perpendicular to the direction of
the field. Due to this, the resultant path of the charged particle is
a helix. The radius of the circular path during the helical motion
is called ‘radius of the helix’. The distance moved by the particle
along the magnetic field during one rotation in the helix is called
‘pitch’.
In the case of a non-uniform magnetic field, the field lines are not
straight. In this case, the helix of the moving charged particle
also follows the direction of the curved magnetic field lines.
During a solar flare a large number of charged particles are
ejected from the sun. When these charged particles enter the
earth’s atmosphere, they get trapped in the earth’s magnetic
field and move in helical paths along the field lines. But near the
earth’s magnetic poles, the density of magnetic lines of force
increases and the density of charges moving in the helical paths
along the magnetic field lines also increases. When the density of
the charge increases at the poles, these particles collide with
each other and also with the molecules of atmospheric gases.
Then the atoms of the atmospheric gases get excited. These
excited atoms emit light during de-excitation. Excited oxygen
atoms emit a green light and excited nitrogen atoms emit a pink
light during de-excitation. This phenomenon when it occurs in
regions of the North Pole is called Aurora Borealis. It is called
Aurora Australis when it occurs in regions of the South Pole.