1.1. Two square, parallel metal sheets are separated by 25 mm in a vacuum, the lower plate being earthed. A narrow beam of electrons enters symmetrically between the plates as shown in Figure 1. There is a uniform magnetic field of flux density 0.020 T, which is perpendicular to the beam and parallel to the plates, acting in the direction shown in Figure 1.  When a potential difference of 1500 V is applied to the plates, the electron beam is undeflected.  

Figure 1

Calculate the speed of the electron, assuming that the electric field between the plates is uniform.

1.2. The potential difference between the plates in Figure 1 can be adjusted. The electrons in the beam are travelling at a speed of 2.35 × 10⁵ m s^-1 when they enter just underneath the top plate in the same direction as before.

If the length of the side of each square plate is 5 cm, calculate the maximum potential difference between the plates which would cause the electron beam to just leave the plates at the opposite side to which it entered without touching the lower plate.

Assume that the electric and magnetic fields only act between the plates

1.3. The northern lights are a phenomenon where the sky glows green due to charged particles from the Sun becoming trapped in the Earth’s magnetic fields near the north pole. 

Some charged particles travel in a circle of radius 50 km in a region where the magnetic flux density is 6.0 × 10^-3 T.

Show that the charged particles causing the northern lights cannot be electrons.