(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 electrically charged sphere of radius, r, and charge, Q, is supported on an insulator in air of permitivity, \(\varepsilon_o\). Write down;
(i) an expression for the electric field intensity on the surface of the sphere;
(ii) an expression for the electric potential at the surface of the sphere;
(iii) a relationship between the electric field intensity and the electric potential at the surface of the sphere
(c) The plates of a parallel plate capacitor, 5.0 x 10\(^{-3}\) m apart are maintained at a potential difference of 5.0 x 10\(^{4}\) V. Calculate the magnitude f the
(i) electric field intensity between the plates
(ii) force on the electron
(iii) acceleration of the elctron
[electronic charge = 1.60 x 10\(^{-19}\)C, mass of electron = 9.1 \times 10\(^{-31}\) kg]
Explanation
(a)(i) Electric potential is the work done in moving a unit positive charge from infinity to a point in an electric field. H is measured in volts or J/C.
(ii) Electric potential energy is the work done or energy required to move a charged particle from infinity to a point in an electric field. The unit is Joules.
(ii) Electric potential unit is in volts v. Electric potential energy is measured in Joules (J)
(b) (i) Electric field intensity E = \(\frac{Q}{4 \pi \varepsilon_or^2}\)
(ii) Electric potential V = \(\frac{Q}{4 \pi \varepsilon_or}\)
(iii) \(\frac{E}{v} = \frac{I}{r}\) OR E = \(\frac{Y}{4 \pi \varepsilon_o r}\)
(c) E = \(\frac{v}{d} = \frac{5 \times 10^4}{5 \times 10^{-3}} = 10^7 v/m\)
(ii) F = qE = 1.6 x 10\(^{-19}\) x 10\(^{7}\) = 1.6 x 10\(^{-12}\) N
(iii) F = ma
a = \(\frac{F}{m}\) = \(\frac{1.6 \times 10^{-12}}{9.1 \times 10^{-31}}\)
= 1.76 x 10\(^{18}\) m/s\(^2\)