Electrons are moving through a vacuum in a narrow beam. The electrons have speed 
. The electrons enter a region of uniform magnetic field of flux density 
. Initially, the electrons are travelling at a right angle to the magnetic field. The path of a single electron is shown in the figure below.
The electrons follow a curved path in the magnetic field. A uniform electric field of field strength 
is now applied in the same region as the magnetic field. The electrons pass undeviated through the region of the two fields. Gravitational effects may be neglected.
Derive a relation between , and for the electrons not to be deflected. Explain your working.
An 
-particle has speed and approaches the region of the two fields along the same
path as the electron. Describe and explain the path of the -particle as it passes through the region of the two fields.
due to the electric field is equal in magnitude and opposite in direction to the force 
due to the magnetic field:
