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

Answer:

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

$W=Fdcos \theta$

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.