(a) (i) Explain (I) electric potential; (II) electric potential energy (ii) State the SI unit of each of the term in (a)(i) above (b) An isolated electrical...

(a)(i)(I) Electric potential at a point in an electric field is the work done in bringing a unit positive charge from infinity to that point.

(a)(i)(II) Electric potential energy of a charge at a point is the work done in bringing that charge from infinity to the point in the electric field.

(a)(ii) SI units: electric potential is measured in the volt (V); electric potential energy is measured in the joule (J).

(b)(i) Electric field intensity at the surface of the charged sphere: \[ E = \dfrac{Q}{4\pi \varepsilon_o r^2}. \]

(b)(ii) Electric potential at the surface of the sphere: \[ V = \dfrac{Q}{4\pi \varepsilon_o r}. \]

(b)(iii) Relationship between them: \[ E = \dfrac{V}{r}\quad(\text{i.e. } V = E r). \]

(c)(i) Electric field intensity between the plates: \[ E = \dfrac{V}{d} = \dfrac{5.0 \times 10^{4}}{5.0 \times 10^{-3}} = 1.0 \times 10^{7}\,\text{V m}^{-1}. \]

(c)(ii) Force on the electron: \[ F = eE = 1.60 \times 10^{-19} \times 1.0 \times 10^{7} = 1.6 \times 10^{-12}\,\text{N}. \]

(c)(iii) Acceleration of the electron: \[ a = \dfrac{F}{m} = \dfrac{1.6 \times 10^{-12}}{9.1 \times 10^{-31}} = 1.76 \times 10^{18}\,\text{m s}^{-2}. \]