# Energy to make a dielectric explode?

• scottKC
In summary, the conversation is about a homework problem involving a block of lucite with a given relative permittivity and a volume of electrons concentrated within it. The goal is to find the bound charge density and surface charge density on the block, as well as the energy stored in the block and the possibility of it exploding. The conversation discusses the relationship between uniform electron density and bound charge, and the difficulty in determining the electric field outside of the electron volume. It is suggested to use the dimensions of the block and make approximations to simplify the problem.
scottKC
i'm working through a homework problem. it has us jump through a few hoops. the premise is that a bunch of electrons are injected into a block of lucite (relative permittivity is supplied). the electrons are all concentrated in a given volume within the block. it asks us for the volume bound charge density in the region of electrons (i'm assuming it is 0, since the electron density is uniform). then asks us for the bound surface charge density on the block (i calculated the free surface charge density at the interface between the region of electrons, then the bound surface charge density in the electron-free region from there).

anyways, the last part of the question is: "What is the energy stored in the block? Could the block explode?"

I'm lost at how to determine this. does anyone have any hints on the physics involved in determining when a dielectric will explode?

What does the uniformity of the electron density has to do with there being no bound charge?

When there is free charge in a dielectric, the dipoles of the dielectric will rearange themselves around the charge, which results in a net bound charge density. Instead of guessing it was 0, why didn't you calculate it? you have all you need:

$$-\nabla \cdot \vec{P}=\rho_b$$
$$\vec{P}=\epsilon_0\chi_e \vec{E}=(\epsilon -\epsilon_0)\vec{E}$$
$$\nabla \cdot \vec{E}= \rho_f/\epsilon$$

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I'm guess I'm just having trouble with this. you're clearly right about the free charge density inducing a bound charge density within the volume injected with electrons (easy to find knowing the free charge density and the relative permittivity). i can find E outside of the electron volume knowing the free charge density. Then with E i can find P (again with the relative permittivity). With P i can find the bound charge density within the electron-free region. I can also find the bound surface density at the face of the block (P dotted with the normal vector).

am i thinking along the correct lines here?

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scottKC said:
I'm guess I'm just having trouble with this. you're clearly right about the free charge density inducing a bound charge density within the volume injected with electrons (easy to find knowing the free charge density and the relative permittivity). i can find E outside of the electron volume knowing the free charge density.

How are you planing on doing this? Or is there a special geometry to this whole thing that allows for an easy determination of the field knowing the charge distribution?

i have the dimensions of the block. it has a 25 square cm face, is 12 mm thick and the electrons are evenly distributed in a 2 mm thickness 6 mm below the surface. now that i think about it, maybe it won't be easy to determine E. i guess I'm missing the connection between a known volume charge density and the surface charge density that it induces. all the examples I've seen involve a conductor and a dielectric together, which is much easier since the conductor itself has a surface charge density.

i get the feeling I'm making this way too difficult on myself. but I'm having a rough time getting a good feeling for dielectrics. maybe if someone could explain what physically will happen in this situation i'll be able to figure it out on my own.

Since the block is much wider than it is tall, you can make the approximation that the slab of charges in the middle produces a field oriented entirely in the z direction. (i.e. you can neglect the border effects and say that at the surface of the block, the field of the slab is pretty much the same as the field of an infnite plane)

In that case, it will be easy to find the field at the surface of the block (and hence P, and hence $\sigma_b$ by use of gauss's law.

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## 1. How is energy used to make a dielectric explode?

Energy is used to make a dielectric explode by creating an electrical field that causes the molecules within the dielectric material to polarize and align. This polarization creates an imbalance of charge within the material, resulting in an increase in voltage and a subsequent explosive discharge of energy.

## 2. What types of energy can be used to make a dielectric explode?

Various forms of energy can be used to make a dielectric explode, such as electrical energy, thermal energy, and mechanical energy. The specific type of energy used will depend on the properties of the dielectric material and the desired outcome.

## 3. Is it safe to make a dielectric explode?

The process of making a dielectric explode can be dangerous and should only be performed by trained professionals in a controlled environment. It involves high levels of energy and can result in a loud and potentially damaging explosion. Safety precautions must be taken to minimize risks.

## 4. What applications require the use of energy to make a dielectric explode?

The use of energy to make a dielectric explode has various applications, including in military and defense technologies, as well as in scientific research and industrial processes. It can also be used in controlled demolition and pyrotechnic displays.

## 5. Are there any potential risks or side effects of using energy to make a dielectric explode?

Using energy to make a dielectric explode can have potential risks and side effects, such as damaging surrounding materials or causing harm to individuals if proper safety precautions are not taken. It is important to carefully assess and manage these risks before conducting any experiments or using this process in practical applications.

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