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

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

Step-by-step 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=(\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 (1)/(2) mv^(2)` this means the speed will not change.