Question

A charged particle moving in a constantmagnetic field always experiences a magnetic force, regardless of its direction of motion. • may experience a magnetic force which will cause its speed to change. • may experience a magnetic force, but its speed will not change

Answer 1

Answer:

A charged particle moving in a constant magnetic field may experience a magnetic force but its speed will not change.

Explanation:

The magnetic force experienced by a charged particle q that moves in a magnetic field $\vec{B}$ with velocity $\vec{v}$ is:

                                                    $\vec{F}=q\vec{v}\ x\ \vec{B}$

and its magnitude is given by:

                                                 $F=q\ v \ B \sin \theta$

where $\theta$ is the angle between the magnetic field and the velocity.

There are two special cases:

• If $v$ and $B$ are parallel $\theta=0$ or opposite $\theta=\pi$ then $sin\ \theta=0$. If the particle moves along magnetic field lines it won't experience a magnetic force.
• If the angle between $v$ and $B$ is $\theta=\frac{\pi}{2}$ the magnetic force has a maximum.

The magnetic force is always perpendicular to the velocity. The work $W$ done by the magnetic force is equal to the force $\vec{F}$ multiplied by the displacement $\vec{dr}$ in the direction of the force:

                                            $W=\vec{F}.\vec{dr}=\vec{F}.(\vec{v}.\Delta t)=0$

Given that the work is equal to the change in kinetic energy $W=\Delta K$ and $K \approx \frac{1}{2} mv^{2}$ this means the speed will not change.