# Meaning of Permittivity as used in EM

1. Aug 17, 2004

### brianparks

Meaning of "Permittivity" as used in EM

Hello all,

I am having difficulty with the concept of permittivity as used in EM contexts. What is it a measure of? What is its physical meaning?

One thing that puzzles me is the relationship between electric field and permittivity:

E = (Q)/(4 * pi * permittivity * r^2)

Using the above equation for electric field, we are forced to conclude that electric field decreases as the permittivity of the medium increases. Is this the right conclusion?

Any help is greatly appreciated,
--Brian

2. Aug 17, 2004

### pervect

Staff Emeritus
The electric field does decrease as the permittivity of the medium increases. This happens physically because dipoles in a physical medium tend to align in such a way that they reduces the total energy of the system. In this low-energy configuration, the electric field is lowered.

If one defines the dielectric constant k = permitivity of medium / $$\epsilon_0$$, a material with a high k will increase the capacitance of a parallel plate capacitor. If one imagines sliding a sheet of high-k material in between the parallel plates while holding the charge Q fixed, one sees that the electric field between the plates decreases, and so does the voltage between the plates. If one pulls the dielectric sheet out again (which requires work), one sees that the voltage between the plates increases again to its original value.

3. Aug 17, 2004

### brianparks

Thanks for the help Pervect,

Tell me if this is right:

Suppose I have a material with a high permittivity. I apply an electric field across it. Positive charges (holes) in the material move toward the negative side of the field, and negative charges (electrons) in the material move toward the positive side of the field. This movement of charges, otherwise known as the displacement current, counters the electric field and therefore reduces its strength. In a vacuum, there is no displacement current, and therefore such a reduction does not occur.

4. Aug 18, 2004

### pervect

Staff Emeritus
If you had holes and electrons moving, you'd be talking about a DC steady-state current flowing through a semiconductor, and you'd be talking about conductance, not about polarization.

Instead of holes and electrons moving, think of little dipoles rotating, as in the picture at

http://hyperphysics.phy-astr.gsu.edu/hbase/electric/dielec.html#c1

Some materials, like water, have a permanent dipole moment, which is always present. However, materials without a permanent dipole moment will develop one in the presence of an electric field, a process called "induced dipole moment".

see for instance
http://hyperphysics.phy-astr.gsu.edu/hbase/electric/diph2o.html

5. Aug 18, 2004

### rayjohn01

The Vacuum also has a permittivity of value eo and displacement currents flow in the vacuum ( this is where radiation such as radio waves originate ) however in this case there is no clear dipoles compared to a physical medium. There are neither hole or electron flows in the vacuum only field motions , but in a medium there is motion of the dipoles ( restricted to the atoms or molecules ) which can be construed as a real
alternating current under alternating field ( ex sinewave ).
Ray

6. Aug 19, 2004

### K.J.Healey

I think of permittivity as the measure of ease of translation of charge in some space. Permeability would then be like the ease of rotation. This also always helps me remember maxwell's eqs (cause of curl only B, etc)

7. Aug 19, 2004

### Claude Bile

The permittivity of a medium describes how much electric field (more correctly, flux) is 'generated' per unit charge. Less electric flux exists in a medium with a high permittivity (per unit charge) due to polarisation effects.

Of course, this is simply the interpretation given by Gauss' Law using words rather than mathematics, and thus not very imaginative!

Claude.