Inserting Dielectric and Direction of Force on It

In summary, the problem involves a slab of width d and dielectric constant K being inserted a distance x into square parallel capacitor plates of side L. The magnitude of the force on the slab is determined to be V0^2*ε0*(K-1)/2d, but there is confusion about the direction of the force. The book, Giancoli, states that the force is towards the left, but the rationalization is that the electric field should be pushing the slab out to the right to attain a lower energy state.
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Homework Statement


A slab of width d and dielectric constant K is inserted a distance x into square parallel capacitor
plates of side L. Determine the magnitude and direction of the force on the slab (Assume V0 is constant.

Homework Equations


F= d/dx(U)
U=1/2CV2

The Attempt at a Solution


I am through determining the magnitude of the force (V020*(K-1)/2d, but am confused as to why the direction of this force is toward the left, which is what my book, Giancoli, says. I have attached a picture with this post.

The way I rationalized it was that because the dielectric raises the capacitance and the potential difference is held constant, the stored energy, U, should be higher with the dielectric, and thus you add energy to the system by putting in the slab. Thus, I would think that the electric field would be trying to push the slab out (to the right) to attain a lower energy state. What am I missing?
 

Attachments

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I understand the force is trying to minimize energy, but why would it be pushing the slab to the left? Thanks for any help.
 

FAQ: Inserting Dielectric and Direction of Force on It

What is a dielectric material?

A dielectric material is a substance that does not conduct electricity, meaning it does not allow an electric current to flow through it easily. It is typically made up of polar molecules, which have a positive and negative charge that can be easily rearranged by an electric field.

How is a dielectric material inserted into an electric field?

A dielectric material can be inserted into an electric field by simply placing it between two objects with opposite charges. For example, it can be placed between two charged parallel plates or between the positive and negative terminals of a battery.

What is the direction of the force on a dielectric material in an electric field?

The direction of the force on a dielectric material in an electric field depends on the polarity of the electric field and the orientation of the material. If the material is placed parallel to the electric field, it will experience a force in the direction of the field. If it is placed perpendicular to the field, it will experience a force in the direction perpendicular to the field.

How does a dielectric material affect the strength of an electric field?

When a dielectric material is placed in an electric field, it polarizes and creates an opposing electric field. This reduces the overall strength of the electric field between the two objects. The amount of reduction depends on the dielectric constant of the material, which is a measure of how easily it can be polarized.

What are some common uses of dielectric materials?

Dielectric materials have many practical applications, such as in capacitors, insulators, and electronic components. They are also used in various industries, including telecommunications, medical technology, and energy production. Additionally, dielectric materials play a crucial role in photovoltaic cells, which convert sunlight into electricity.

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