An air-filled capacitor is formed from two long conducting cylindrical shells that are coaxial and have radii of 48 mm and 84 mm.The electric potential of the inner conductor with respect to the outer conductor is -400 V.(k = 1/4πε₀ = 8.99 × 10⁹ N • m²/C²)The energy stored in a 1.0-m length of this capacitor is closest to A) 8.0 μJ. B) 5.7 μJ. C) 11 μJ. D) 16 μJ. E) 22 μJ.

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Quizplus · Accepted Answer

The capacitance of a cylindrical capacitor is given by:$$C = 2\pi\epsilon_0\frac{L}{ln(b/a)}$$where:* C is the capacitance in farads (F)* $\epsilon_0$ is the permittivity of free space (8.85 x 10^-12 F/m)* L is the length of the capacitor in meters (m)* a is the radius of the inner conductor in meters (m)* b is the radius of the outer conductor in meters (m)In this problem, we have:* L = 1.0 m* a = 48 mm = 0.048 m* b = 84 mm = 0.084 m* V = -400 VSubstituting these values into the equation above, we get:$$C = 2\pi(8.85 x 10^-12 F/m)\frac{1.0 m}{ln(0.084 m/0.048 m)} = 2.24 x 10^-11 F$$The energy stored in a capacitor is given by:$$U = \frac{1}{2}CV^2$$Substituting the values of C and V into this equation, we get:$$U = \frac{1}{2}(2.24 x 10^-11 F)(-400 V)^2 = 8.0 \mu J$$Therefore, the energy stored in a 1.0-m length of this capacitor is closest to 8.0 μJ.

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