A particle of mass $m$, charge $+q$ and speed $v$ is moving parallel to a uniform gravitational field of strength $g$. State the magnitude and direction, if any, of the force on the particle.
State the magnitude and direction, if any, of the force on the particle when the particle is travelling along the direction of a uniform magnetic field of flux density $B$.
Two charged horizontal metal plates, in a vacuum, create a uniform electric field of field strength $E$ between the plates. The field strength outside the region between the plates is zero. The particle in (a) enters the electric field region at right angles to the field direction, as shown in Fig. 6.1. A uniform magnetic field is to be added in the same region as the electric field so that the particle travels through the space between the plates without deflection. State and explain the direction of the magnetic field.
Derive, with explanation, the relation between the speed $v$ and the magnitudes of the electric field strength $E$ and the magnetic flux density $B$.
A second particle has the same mass $m$ and charge $+q$ as the particle in (b), but its speed is $2v$. This particle enters the region between the plates in the same direction as the particle in (b). On Fig. 6.1, sketch the path of this particle in the region between the plates.