# Dielectric inserted in parallel plate capacitor

• PP27
In summary, when a dielectric is partially inserted between two plates of a disconnected capacitor, there will be a fringing field which causes the dielectric to move towards the center of the capacitor. When the capacitor is connected to a battery, the force on the dielectric can be calculated using the principle of virtual work, taking into account the change in stored energy and the energy from the connected battery. A diagram can also be used to visualize the qualitative effect of free charges and induced charges on the dielectric's surfaces.
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?

## 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?

PP27 said:
inserted between two plates of a capacitor that is disconnected
Charged? Or, uncharged?

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.

## 1. What is a dielectric material?

A dielectric material is a type of insulating material that can be inserted between the plates of a parallel plate capacitor to increase its capacitance. Dielectric materials have a high resistance to the flow of electric current and are often used to store electrical energy in capacitors.

## 2. How does a dielectric material affect the capacitance of a parallel plate capacitor?

When a dielectric material is inserted between the plates of a parallel plate capacitor, it increases the capacitance of the capacitor. This is because the dielectric material reduces the electric field between the plates, allowing for a greater amount of charge to be stored on the plates.

## 3. What are some common examples of dielectric materials?

Some common dielectric materials include air, glass, plastic, ceramic, and paper. These materials have high resistivity and low conductivity, making them effective insulators for use in capacitors.

## 4. How does the thickness of a dielectric material affect the capacitance of a parallel plate capacitor?

The capacitance of a parallel plate capacitor increases with the thickness of the dielectric material. This is because a thicker dielectric material allows for a greater amount of charge to be stored on the plates, resulting in a higher capacitance.

## 5. Can a dielectric material be used to decrease the capacitance of a parallel plate capacitor?

Yes, a dielectric material with a low dielectric constant can be used to decrease the capacitance of a parallel plate capacitor. This is because the low dielectric constant reduces the amount of charge that can be stored on the plates, resulting in a lower capacitance.

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