# PHY C22: Charged Particles in Electric & Magnetic Fields

A tough one (but an interesting one!):

• Velocity selection
• Hall voltage

What happens when a charged particle enters an electric field AND a magnetic field?
In my fields post, I mentioned that when multiple fields act on an object, the object will experience the SUM of those forces. The same applies here:

## All you have to do is find the net force, which will dictate how the particle will accelerate & deflect.

One application of this is:

# Velocity Selection

What is a velocity selector?
A device used to produce a beam of particles all travelling at the same specific velocity.

It contains perpendicular magnetic & electric fields, with a beam of particles entering perpendicular to both:

How does it work?

In general,

Fnet = FE – FB
Fnet = qV – Bvq

### Fnet = q(V – Bv)

For particles which pass through the selector undeviated:

## v = E/B

This has a few implications for velocity selectors:

• mass does not affect the net force acting on a particle:
• particles of the selected velocity WILL pass through regardless of their mass
• charge only affects the net force acting on a particle when it is non-zero:
• particles of different charge will have different paths IF they are deviated, but all particles at the selected velocity WILL pass through undeviated regardless of their charge

*You must also be able to identify the direction of deviation for particles at velocities above or below the selected velocity. Just use Fnet = q(V – Bv) & identify the direction of the net force. Remember to check the direction each force effects the particle!

We have seen how charged particles react to the presence of magnetic & electric fields. But now, we will investigate how the deflection of the charged particles themselves creates an electric field:

# The Hall Effect

## Hall Voltage VH = BI/ntq

How can we apply this?
In a Hall probe.

• It works by:
• providing a thin slice of a conductor which can be placed perpendicular to a magnetic field
• a Hall Voltage is created between the sides of the slice
• the VH across these 2 terminals is measured
• the value of B can be calculated by rearranging VH = BI/ntq (I, n, t, & q are specific to that Hall probe)
• It can be optimised by increasing VH for a given B (to reduce % error). This is done by:
• reducing the value of n: a semiconductor is used instead of a metal (less number density of charge carriers)
• reducing the value of t: slice is made to be thin as possible