Question

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?

Answer 1

K remains constant

Step-by-step 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

`W=Fdcos \theta`

where F is the magnitude of the force, d is the displacement of the particle, and
`\theta` 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
`\theta=90^(\circ)` and
`W=0`, 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:

`\Delta K=W`

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