Problem $10$:$$ An air$-$filled parallel$-$plate capacitor is connected to a voltage source until it is fully charged. The voltage source is disconnected leaving the charge on the capacitor plates.

Part $($a$)$ A voltmeter indicates that the voltage across the charged capacitor is $48\mathrm{.}6$VV$.$ When a dielectric material is inserted between the plates completely filling the gap, the reading on the voltmeter drops to $11\mathrm{.}2$VV$.$ What is the dielectric constant of the dielectric material?

Part $($b$)$ If the dielectric material is slowly extracted until it fills only $15\%\%$ of the gap, then what is the reading, in volts, on the voltmeter?