An air-filled capacitor is formed from two long conducting cylindrical shells that are coaxial and have radii of 13 mm and 85 mm.The electric potential of the inner conductor with respect to the outer conductor is -600 V.(k = 1/4πε₀ = 8.99 × 10⁹ N • m²/C²)The maximum energy density of the capacitor is closest to A) 2.7 × 10^-3 J/m³. B) 1.3 × 10^-3 J/m³. C) 6.7 × 10^-4 J/m³. D) 3.4 × 10^-3 J/m³. E) 1.7 × 10^-4 J/m³.

Question

Quizplus · Accepted Answer

The maximum energy density in a capacitor is given by $ u = \frac{1}{2} \varepsilon_0 E^2 $, where $ E $ is the electric field. For a cylindrical capacitor, $ E = \frac{V}{r \ln(b/a)} $, where $ V $ is the potential difference, $ r $ is the radial distance, and $ a $ and $ b $ are the radii of the inner and outer cylinders, respectively. The maximum energy density occurs at the inner surface, where $ r = a $. Substituting the given values and calculating, the maximum energy density is closest to 2.7 × 10^-3 J/m³.

An Air-Filled Capacitor Is Formed from Two Long Conducting Cylindrical