# Question #7bdc8

Sep 12, 2016

Yes. A charged particle may be accelerated by a magnetic field. However, this acceleration is by changing the direction of the velocity vector of the charge.

The magnetic field cannot change the speed of the charge.

#### Explanation:

The magnetic force on the charge q is given by,

$\vec{F} = q \vec{v} X \vec{B}$ where $\vec{v}$ is the velocity vector.

The force is always perpendicular on the plane of the magnetic field and velocity vector. Thus, it can change the trajectory of the particle.

For example, it can make the charge move in a helical trajectory.

But, since $\vec{F} \cdot \vec{v} = \frac{\mathrm{dT}}{\mathrm{dt}}$ where $T$ is the kinetic energy.

Force is perpendicular to velocity, the dot product vanishes which implies $\frac{\mathrm{dT}}{\mathrm{dt}} = 0$

Thus, $T = C o n s t .$

Since, $T = \frac{1}{2} m {v}^{2}$ this implies $v$ is also a constant. Thus, the force cannot change the speed (magnitude of velocity).