Question

Derive motion in a magnetic field.

Answer 1

hey mate ; )

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The period of circular motion for a charged particle moving in a magnetic field perpendicular to the plane of motion is. Helical motion results if the velocity of the charged particle has a component parallel to the magnetic field as well as a component perpendicular to the magnetic field.

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hope it helps ^_^

Answer 2

A magnetic field B exerts a force on an electrically charged particle according to the Lorentz force law, given by: F=q(vxB). The force being always perpendicular to the direction of velocity, the trajectory of the particle is circular if there is no component of velocity parallel to the magnetic field. The direction of the circle(clockwise or anticlockwise) will be such that F always points towards its center. If there is a component of velocity parallel to the magnetic field, the particle moves in a helix, with the axis of the helix along the direction of the magnetic field( the velocity component parallel to the magnetic field is unchanged by the Lorentz force, because vxB=0).

The following images illustrate the theory explained above:

Here, B is pointing into the plane of the page