Dielectric inserted in parallel plate capacitor

[PP27]

Homework Statement

When a dielectric is partially inserted between two plates of a capacitor that is disconnected, what will be it's motion? Also what will be its motion if the capacitor is connected to a battery?

Homework Equations

The Attempt at a Solution

For the first part. I think the lines of electric field are not uniform in the part of the dielectric outside the region of the parallel plate capacitor. So, there will be fringing field which makes dielectric move towards the centre of the capacitor. But i can't figure out what will be the effect when capacitor is connected to the battery?

 

[Bystander]

inserted between two plates of a capacitor that is disconnected

Charged? Or, uncharged?

 

[rude man]

You can draw a diagram with the free charges on the top & bottom plates and the induced charges on the dielectric's surfaces to get a qualitative idea of what must happen.

Quantitatively, you need to analyze the problem separately for disconnected and battery-connected capacitors. You can compute the force incl. its direction for the disconnected case pretty readily; use the principle of virtual work to compute the force on the dielectric. "Virtual work" here means you move the dielectric a given distance into the capacitor and you calculate the resultant change in E field stored energy

For the connected case you still compute v. work but now you also need to take into account the fact that the connected battery enters the energy equation.