Variable Capacitor in an Old-Fashioned Radio

Question:
An old-fashioned radio is tuned by means of a variable capacitor whose capacitance varies through 10 < C < 100 pF as the shaft is rotated through 0 < θ < π.

a) The potential across the capacitor is maintained at Φ = 100 V . Show that the torque on the shaft is

What is the value of the torque?


b) The capacitor is rotated to θ=π (C=100 pF), charged to Φ = 100 V , and the voltage source disconnected. The capacitor is then rotated to θ=0 (C=10 pF). What is the voltage on the capacitor now? What is the energy in the electric field?

c) The capacitor is rotated to θ=π (C=100 pF) and charged to Φ = 100 V . The capacitor is then rotated to θ=0 (C=10 pF) with the voltage source connected. What is the energy in the electric field now?

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