Question

A capacitor is formed from two long conducting cylindrical shells which arc coaxial, and have radii of 25 mm and 100 mm. The electric potential of the inner conductor with respect to the outer conductor is -500 V. How much energy is stored in a 1.0 m long section of the capacitor?

Answer 1

Taking the dielectric constant (k) of air as 1, the capacitance per metre is 2πε₀ / ln(b/a) See link.

For a 1m length:

ε₀=8.85 × 10^^-12 C^² N^^-1 m^^-2.

C = 2πε₀ / ln(100/20) = 3.46 x 10^⁻¹¹ F

Energy stored = ½CV^² = ½ x 3.46 x 10^⁻¹¹ x 500^² = 4.32x10^⁻⁶ J