A cylindrical capacitor is constructed using two coaxial cylinders of the same length 10 cm and of radii 2 mm and 4 mm. (a) Calculate the capacitance. (b) Another capacitor of the same length is constructed with cylinders of radii 4 mm and 8 mm. Calculate the capacitance.
(a) The capacitance of a cylindrical capacitor is given by `C = (2pi∈_0l)/(In(R_2/R_1)`
⇒ `C = (2 xx 3.14 xx 8.85 xx 10^-12 xx 0.10)/("In" 2)`
⇒ `C = 8 "pF" (∵ "In" 2 = 0.693)`
(b) When a capacitor of the same height with cylinders of radii 4 mm and 8 mm is taken, its capacitance comes to 8 pF, which is the same as above because the ratio of the radii is the same.