A 0.350-m-long cylindrical capacitor consists of a solid conducting core with a radius of 1.20 mm and an outer hollow conducting tube with an inner radius of 2.00 mm. The two conductors are separated by air and charged to a potential difference of 6.00 V. Calculate (a) the charge per length for the capacitor; (b) the total charge on the capacitor; (c) the capacitance; (d) the energy stored in the capacitor when fully charged.
Introduction We have to first calculate the charge per unit length of the given cylindrical capacitor. Then we have to calculate the total charge of the capacitor, the capacitance of the capacitor and finally we have to calculate the energy stored in the capacitor. Step 1 The charge per unit length of the capacitor is given by Here k is the dielectric constant of the medium and is 1 for air. is the permittivity of the 0 vacuum and a and b are the radius of the core and inner radius of the hollow outer cylinder. And V is the voltage connected. Now we know that k = 1, 0= 8.85 × 10 12F/m, a = 1.20 mm = 1.20 × 10 3 m, b = 2.00 mm = 2.00 × 10 3 m, and V = 6.00 V. Hence the charge per unit length is given by So the charge per unit length of the capacitor is 6.53 × 1C/m.