Investigating the Absorption of Radiation in Matter using G-M Counter

 Abstract

In this experiment we will investigate the nature of the interaction between an external electrostatic field and the induced polarization charge in a liquid between the plates of a capacitor and determine the dielectric constant of a liquid oil. We find that the dielectric constant of the oil used in the experiment is equal to ε_r = 4.19 with percentage error equal to 10.85 %.

Introduction 

Matter, of course, comes in many varieties-solids, liquids, gases, metals, woods, glasses-and these substances do not all respond in the same way to electrostatic fields. Nevertheless, most everyday objects belong (at least, in good approximation) to one of two large classes: conductors and insulators (or dielectrics). Conductors: these are substances that contain an "unlimited" supply of charges that are free to move about through the material. In practice what this ordinarily means is that many of the electrons (one or two per atom in a typical metal) are not associated with any particular nucleus, but roam around at will. In dielectrics, by contrast, all charges are attached to specific atoms or molecules-they are on a tight leash, and all they Can do is move a bit within the atom or molecule. Such microscopic displacements are not as dramatic as the wholesale rearrangement of charge in a conductor, but their cumulative effects account for the characteristic behavior of dielectric materials. There are actually two principal mechanisms by which electric fields can distort the charge distribution of a dielectric atom or molecule: stretching and rotating

If the substance consists of neutral atoms (or nonpolar molecules), the field will induce in each a tiny dipole moment, pointing in the same direction as the field. If the material is made up of polar molecules, each permanent dipole will experience a torque, tending to line it up along the field direction. (Random thermal motions compete with this process, so the alignment is never complete, especially at higher temperatures, and disappears almost at once when the field is removed.)

Notice that these two mechanisms produce the same basic result: a lot of little dipoles pointing along the direction of the field-the material becomes polarized.

A convenient measure of this effect is P = dipole moment per unit volume, which is called the polarization. From now on we shall not worry much about how the polarization got there. Actually, the two mechanisms we described are not as clear-cut as we tried to pretend. Even in polar molecules there will be some polarization by displacement (though generally it is a lot easier to rotate a molecule than to stretch it, so the second mechanism dominates). It is even possible in some materials to "freeze in" polarization, so that it persists after the field is removed.

Now what will happen if we put a dielectric material between a parallel plate capacitor? If we put a dielectric material ( suppose it will be a slap) between the plates of a capacitor it will pull into the space between the plates of a parallel-plate capacitor (tends to fill the capacitor space) when a potential difference is established between the plates. If the electrostatic field were strictly uniform between the plates and zero outside, no electrostatic force would be exerted on the dielectric slab, since then the field is always perpendicular to the plates and there would be no force component to pull the slab into the capacitor space in such a case. Consequently, the origin of the electrostatic force is the interaction of the fringing field near the edges of the plates with the surface polarization charge in the dielectric as in figure 1 and figure 2.

Since the electrostatic forces acting on the surface polarization (σP = P.n) charge are not collinear, they result in a net force directed parallel to the plates which consequently pulls the dielectric slab into the capacitor space. For a homogeneous linear dielectric with no free charges, the volume polarization charge is zero and does not contribute to the net force acting on the dielectric.

The same thing happens to a capacitor immersed in a liquid Figure 3. As the potential difference is applied between the capacitor plates, the liquid rises in the capacitor to a height h above its initial level due to the electrostatic force. The liquid level reaches equilibrium when the weight of the carried liquid equals the electrostatic upward pull.

Methodology

Procedure

1. Arrange the travelling microscope and the cell containing the oil in such a way that the microscope moves perpendicular to the plates and measure the separation between the plates of the capacitor. Repeat the measurement at different positions of the plates and evaluate the average separation.

2. Rearrange the apparatus in such a way that the microscope moves up and down. Leave the liquid in the cell for a while until its level between the plates is stable.

3. Without any potential difference applied to the capacitor determine the level of liquid between the plates and use it as the reference position with respect to which subsequent heights of the liquid between the plates are determined (notice that the image is inverted).
4. Apply a 0.5 kV potential and determine the position of oil level between the plates. Do not touch the connecting leads or the power supply metallic parts during this procedure (it is dangerous due to high voltages).
5. Repeat the step (4) for voltages up to 3.0 kV (step of 0.5 kV). Tabulate your results.
6. Turn the high voltage down to zero. The voltmeter reading may still be above zero (why?). Shunt the two terminals of the voltmeter by a connecting wire to ensure that the reading is back to zero.
7. Wait for a while until the liquid level is stable, and repeat steps (4) and (5) to obtain another set of data.

Formalism

The capacitance of the capacitor is then given by:

      C =  (𝜀₀ 𝑤 / 𝑑) {𝜀𝑟𝑥 + (𝑙 - 𝑥)} ……… (1)

The electrostatic energy stored in the capacitor is:

U = (1/2)(Q^2/C) ...............(2)

the electrostatic force acting on the dielectric with dielectric constant ε_r is given by:

The height of the liquid above its original level is then given by:

Data Analysis:

V(kv)	h(cm)	∆ h	V2
0	12.353	0	0	h0
0.5	12.405	0.052	0.25	h1
1	12.503	0.15	1	h2
1.5	12.601	0.248	2.25	h3
2	12.701	0.348	4	h4
2.5	12.803	0.45	6.25	h5
3	13.002	0.649	9	h6

The d-spacing between the plate of capacitor:

d₁ = 12.6 + 0.002 =12.602 cm

d₂ = 12.752+0.002 = 12.754 cm

  ∆ = d₂ – d₁ = 0.15 cm.

ε_r = 4.19

 

Discussion And Conclusion

Just as a conductor is attracted into an electric field , so too is a dielectric-and for essentially the same reason: the bound charge tends to accumulate near the free charge of the opposite sign and we see that in a slab of linear dielectric material, partially inserted between the plates of a parallel-plate capacitor.  We have always pretended that the field is uniform inside a parallel-plate capacitor, and zero outside. If this were literally true, there would be no net force on the dielectric at all since the field everywhere would be perpendicular to the plates. However, there is in reality a fringing field around the edges. which for most purposes can be ignored but in this case is responsible for the whole effect. This fringing field pulls the dielectric into the capacitor.

References:

◼ Griffiths , Introduction to electrodynamics , third edition.

◼ Manual of the advanced practical physics , University Of Jordan.