Rotary variable capacitor

A variable capacitor consists of two metal semicircles of radius \(R\) with vertical separation \(d.\) The capacitor is charged when \(\varphi=0,\) and is then disconnected from the voltage source. The discs are then rotated through the angle \(\varphi = 90^\circ.\)

How does the rotation change the energy that's stored in the capacitor?

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