Question

An air-filled capacitor is formed from two long conducting cylindrical shells that are coaxial and have radii of 13mm and 85mm. The electric potential of the inner conductor with respect to the outer conductor is -600V. The maximum energy density of the capacitor is closest to __________________.

Please provide work and an explanation! I have attempted this problem multiple times and can't seem to get it right. Thanks!

Answer 1

Electric field, E = q/(2 pi rL e0)

Capacitance, C = (2 pi L e0)/ln(b/a)

Charge, q = (2 pi e0 LV)/ln (b/a)

E = V/[a ln(b/a)]

E = 600/[0.013 ln(85/13)]

E = 24580 V/m

Energy density, J = 0.5 e0 E^2

J = 0.5 x 8.85 x 10^-12 x 24580^2

J = 2.7 x 10^-3 J/m^3

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