Define electric potential at a point in terms of work done.
A charged particle starts from rest in a vacuum and is accelerated through a potential difference $V$. Show that the final speed $v$ of the particle is given by $v = \sqrt{\frac{2Vq}{m}}$, where $\frac{q}{m}$ is the charge-to-mass ratio (the specific charge) of the particle.
A particle with specific charge $+9.58 \times 10^{7}\,\text{C kg}^{-1}$ is travelling in a vacuum towards a fixed metal sphere, as shown in Fig. 4.1. Its initial speed is $2.5 \times 10^{5}\,\text{m s}^{-1}$ when it is a long distance from the sphere. The sphere is positively charged and has a potential of $+470\,\text{V}$. Use the expression in (b) to determine whether the particle will reach the surface of the sphere.