A cylindrical capacitor has two co-axial cylinders of length 15 cm and radii 1.5 cm and 1.4 cm. The outer cylinder is earthed and the inner cylinder is given a charge of 3.5 µC. Determine the capacitance of the system and the potential of the inner cylinder. Neglect end effects (i.e., bending of field lines at the ends).
Step 1 : Electric field inside capacitor For safety, the field intensity never exceeds 10% of the dielectric strength. Hence, electric field intensity, E=10% of 107 V/m =106 V/m Given V=1kV=1000V We know that, V=E×d ∴ Distance between the plates d=EV=1061000=10−3m Step 2: Capacitance Given, Capacitance C=50pF Also, C=dKAεo Dielectric constant of material, K=3 ∴ A=εoKCd=8.85×10−12×350×10−12×10−3≈19 cm2
