# Motion in a Magnetic Field

Motion in magnetic field of a charged particle is characterized by the change in the direction of motion. It is expected also as magnetic field is capable of only changing direction of motion of the charge particle when it is in motion in a magnetic field. Here we assume magnetic field uniform. This assumption helps to simplify the description and lets us easily visualize the motion of a charged particle in magnetic field.

## Different Cases of Motion in a Magnetic Field:

Let us the discuss motion in a magnetic field of a charge particle. There are three cases arise:

Case I: If the charge particle enters in the magnetic field in the parallel or antiparallel direction to the magnetic field.

A moving charge particle does not experience any force if its motion is parallel or antiparallel to the direction to the magnetic field. Because according to the Lorentz force the F = q v B Sin θ,so in this case if the θ = 0° or 180°, then the value of Sin θ = 0. Thus, the value of Lorentz force is zero. There is no deflection in the motion of a charged particle in a magnetic field.

Case II: If the charge particle enters in the magnetic field at the right angle to the magnetic field.

Let us consider that the charge particle having charge q enters in the magnetic field B with velocity v at the right angle to the magnetic field.

According to the Lorentz force,

F = q v B Sin 90°

F = q v B

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The direction of the Lorentz force is always perpendicular to the direction of motion and magnetic field both. We can find the direction of Lorentz force by using Fleming’s right hand rule.

Thus, the path of the charge particle when it is in motion in magnetic field is circular.

If we consider that the mass of the charge particle is m and r be the radius of the circular path, then the necessary centripetal force required by the charge particle to move in the circular path is Mv2/r The Lorentz force provides this centripetal force.

q v B = Mv2 / r

r = Mv / qb

Thus, the radius of the circular path is directly proportional to the speed of the charge particle and the mass of the charge particle when it is in motion in a magnetic field.

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