Question

You are working with a team to design a better electron microscope. To precisely control the beam of electrons, your team decides to use a magnetic field produced by current. For your study you decide to use a Cathode Ray Tube (CRT) with a magnetic field perpendicular to its axis. The magnetic field will be produced by Helmholtz coils, two parallel coils of wire with the distance between them equal to their radius. Before you can evaluate the sensitivity of the electron microscope design, you need to determine how the magnitude of a constant magnetic field affects the position of the beam spot.

a. Draw a picture of the CRT in the Helmholtz coils. Since you will not be using electric fields, do not include the deflection plates in your sketch. Be sure you have all the other components in your sketch. Draw a coordinate axis on this sketch and show the magnetic field direction and the region occupied by the magnetic field. Draw the electron trajectory through all regions of the CRT together with its velocity andacceleration. Draw the electron trajectory if there were no magnetic field. The difference between where these two trajectories hit the CRT screen is the deflection.
b. What path does an electron follow while traveling through a constant magnetic field? The magnetic force is always perpendicular to the electron

Answer 1

1) see picture

2) ⇒ force = 0

⇒ f = evB

3)
`v = \sqrt{(2e\delta v)/(m)}`

4)
`v_m = (eBr)/(m)`

Step-by-step explanation:

See attached for detailed workings.

Answer 2

Answer and Explanation:

(a) The attached image below shows the diagram of a CRT in the helmholtz coils and well labelled with details

(b). The electron will follow a circular path which travels along under constant magnetic field

`r = (mV)/(qB)`

where m = mass of electron, V = velocity of electron, q = charge of the electron and B = magnetic field strength