A cylindrical capacitor is made of two thin-walled concentric cylinders. The inner cylinder has radius r₁ = 4.0 mm, and the outer one a radius r₂ = 8.0 mm. The common length of the cylinders is L = 150 m. What is the potential energy stored in this capacitor when a potential difference 4.0 V is applied between the inner and outer cylinder? (k = 1/4πε₀ = 8.99 × 10⁹ N ∙ m²/C²) A) 9.6 × 10^-8 J B) 1.3 × 10^-8 J C) 6.3 × 10^-8 J D) 0.34 × 10^-8J E) 4.6 × 10^-8 J

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Quizplus · Accepted Answer

The potential energy stored in a cylindrical capacitor is given by:$$U = \frac{1}{2}CV^2$$where C is the capacitance of the capacitor and V is the potential difference applied between the inner and outer cylinder.The capacitance of a cylindrical capacitor is given by:$$C = \frac{2\pi\varepsilon_0 L}{\ln(r_2/r_1)}$$where ε0 is the permittivity of free space, L is the common length of the cylinders, and r1 and r2 are the radii of the inner and outer cylinders, respectively.Substituting the given values into the equations for C and U, we get:$$C = \frac{2\pi(8.99 imes 10^9 N \cdot m^2/C^2)(150 m)}{\ln(8.0 mm/4.0 mm)} = 1.11 imes 10^{-10} F$$$$U = \frac{1}{2}(1.11 imes 10^{-10} F)(4.0 V)^2 = 9.6 imes 10^{-8} J$$Therefore, the potential energy stored in the capacitor is 9.6 × 10^-8 J.

A Cylindrical Capacitor Is Made of Two Thin-Walled Concentric Cylinders