Consider a horizontal square plate capacitor of area 1*1m 2 , capacitance in vac

Question

Consider a horizontal square plate capacitor of area 1*1m2, capacitance in vacuum 4 F, which contains adielectric material with dielectric constant K=3. The dielectricslides frictionlessly and is attached via a massless string and amassless pulley to a block of mass 1.5 kg. The block pulls thedielectric from the capacitor as it falls. Compute the speed of theblock at the instant the dielectric leaves the capacitor assumingit starts at rest and that the voltage across the capacitor afterthe dielectric is removed is measured to be 200 V.

Explanation / Answer

Energy of a capacitor --no dielectric. E=U^2C/2 --with dielectric. E=U^2C/2K where U and C be the voltage and capacitance in vacuum of thecapacitor. Energy is conseved. so U^2C/2K=-l*g*m+U^2C/2+mv^2/2 lgm - U^2C/3 =mv^2/2. so v=sqrt(2lg-2U^2C/3m)=4,419(m/s)

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