Figure shows in schematic form an electrostatic voltmeter, a capacitive system consisting of a fixed electrode and a moveable electrode. The moveable electrode is connected to a vane which rotates on a pivot such that the air gap between the two electrodes remains fixed as the vane rotates. The capacitance of this system is given by A torsional spring is connected to the moveable vane, producing a torque T _spring = ? K (? - ?₀)

a. For 0 ? a or using the results of Problem 3.19, derive an expression for the electromagnetic torque T_fld in terms of the applied voltage V_dc.

b. Find an expression for the angular position of the moveable vane as a function of the applied voltage V_dc.

c. For a system with R = 12 cm, d = 4 cm, g = 0.2 mm, ? = ?/3 rad, ?₀ = 0 rad , K = 3.65N.m/rad Plot the vane position in degrees as a function of applied voltage for 0 V_dc 1500 V.

o Rd(a 101) C(e) (0> lel) Fixed electrode /2 Vane Torsional spring Moveable electrode Depth d into paper