Notes On Motion Of A Charged Particle In An External Magnetic Field - CBSE Class 12 Physics
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.

#### Summary

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.

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