Question 4 a)

In

some experiments, scientists want to make sure that the charged

particles entering the experiment (e.g. a beam) have the same velocity.

For this, they can use a velocity selector, which has a region of

uniform electric and magnetic fields that are perpendicular to each

other and perpendicular to the motion of the charged particles. Both the

electric and magnetic fields exert a force on the charged particles. If

a particle has precisely the right velocity, the two forces exactly

cancel and the particle is not deflected.

Equating the forces due to the electric field and the magnetic field gives the following equation:

Solving for velocity, we get:

A

particle moving at this velocity will pass through the region of

uniform fields with no deflection, as shown below. For higher or lower

velocities than this, the particles will feel a net force and will be

deflected. A slit at the end of the region allows on the particles with

the correct velocity to pass.

Suppose a particle with twice the velocity of the particle above enters the velocity selector. The path of this particle will curve: