R-ATPHY-36

Graph

Charged particles in E and B field

Before relativity in electric fields

$$\begin{align} W=Vq \\ F=qE \\ E=\frac{V}{d} \\ qV=\frac{1}{2}mv^2 \end{align} $$

Hence, when we place a charged particle in an electric field, it is accelerated, and gains kinetic energy(work is done on it).

Very hard to do things with neutral particles :(

Note, this can be very fast. Consider having to use $Vq=mc^2\left(\frac{1}{\sqrt{ 1-\frac{v^2}{c^2} }}-1 \right)$ to accurately determine the kinetic energy of the particle.

Hence, we can also use electric fields to change the direction of particles. Note, this is a parabolic trajectory (woops, no $r=\frac{mv}{qB}$)

Magnetic fields

Remember, $F=qvB\sin \theta$

This time, the direction is circular.

Velocity selector

Here, the magnetic force is upwards, the electric force is downwards. insert some math $v=\frac{E}{B}$

If the velocity is too fast, the magnetic force will 'win' and it hits the top plate.
If the velocity is too slow, the electric force will 'win' and it hits the bottom plate.

Cathode Ray Tube

Use in old technology to create images on tv! Its like lighting up a pixel on a screen. But a bit complex.

Linear accelerator (LINAC)

Mass spectrometer

Why heavy deflected less:

$$\begin{align} qvB=\frac{mv^2}{r} \\ r=\frac{mv}{qB} \end{align} $$

So for heavier things, $m\uparrow$ $\implies$$r \uparrow$, hence it has a greater arc and appears to be deflected less :)

Cyclotron

$$\begin{align} qvB=\frac{mv^2}{r} \\ v=\frac{qBr}{m} \\ \frac{2\pi r}{T}=\frac{qbR}{m} \\ f=\frac{1}{T}=\frac{qB}{2\pi m} \end{align} $$

i.e. the frequency of a charged particle of fixed mass moving in circular motion through the cyclotron is constant!

If the frequency changed, then things would be quite annoying. :(
Note: The cyclotron reverses the field to create that centripetal acceleration towards the centre.

A problem (with cyclotrons)

These things be going really fast. But with relativity, velocity and momentum change. This means that $f$ is no longer constant! Uh oh, things start to mess up. (Fail at 1% speed of light)

Synchrotron

This produces high speed electrons! :)

We can harness the electron's energy to produce electromagnetic radiation of various frequencies.

When electrons lose energy (or oscillate) they emit electromagnetic radiation.

Visible: better than laser, can get any frequency you choose (lasers use specific band gap)
X-rays: any frequency we want, so yay!