An ion of the solar wind becomes trapped by the earth’s magnetic field. how will the magnetic field affect the kinetic energy k of the ion?

K remains constant

Explanation:

The magnetic force does not do any work on the ion.

In fact, the magnetic force due to a magnetic field is always perpendicular to the motion of the charge itself. Keep in mind that the work done by a force is given by

where F is the magnitude of the force, d is the displacement of the particle, and is the angle between the direction of the force and the displacement. Since the magnetic force is perpendicular to the displacement of the ion, then and , so the work done is zero.

For the work-energy theorem, the work done on the ion is equal to the variation of its kinetic energy:

However, since W=0, then , which means that the kinetic energy of the ion does not change.

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