Question

A cylindrical capacitor has tow co-axial cylinders of length 20 cm and radii 1.5 cm and 1.6 cm. The outer cylinder is earthed and inner cylinder is given a charge 4μC. The capacitance of the system is (neglect end effect)

A. 2.8×10⁻⁸F
B. 4.2×10⁻¹⁴F
C. 1.7×10⁻¹⁰F
D. 3.4×10⁻¹²F

Answer 1

The capacitance of the cylindrical capacitor is approximately 4.2x10^-14 F (option B).

Step-by-step explanation:

The capacitance of a cylindrical capacitor can be calculated using the formula:

C = (2πε₀l) / ln(R₂ / R₁)

where C is the capacitance, ε₀ is the permittivity of free space (8.85x10-12 F/m), l is the length of the cylinders, and R₁ and R₂ are the radii of the inner and outer cylinders respectively.

In this case, the length is given as 20 cm and the radii are given as 1.5 cm and 1.6 cm. Substituting these values into the formula, the capacitance can be calculated to be approximately 4.2x10-14 F (option B).