# Have i got the DIFFERENCE BETWEEN PERMITTIVITY AND PERMEABILITY Right?

1. Jul 25, 2014

### BINNOY.S.P

Hi,
Just wanted to know the difference between permittivity and permeability.

As far as I researched, permittivity is resistance to the creation of electric field and permeability is like an allowance of a medium to the creation of a magnetic field. Is it right?

I get confused because in some of the equations, both pemittivity and permeability occur in the numerator . That boggles me.

Like
2E = -ω2.μ.ε.E

it should be E bar above. But i dont know how to but a bar. The example is known as Helmhotz equation something.

BINNOY

2. Jul 25, 2014

### vanhees71

The trouble is caused by historical confusion about the physical meaning of the em. field componentents in matter. Nowadays, having relativity at hand, we know that $\vec{E}$ and $\vec{B}$ as well as $\vec{D}$ and [/itex]\vec{H}[/itex] belong together, while traditionally people thought one should associate $\vec{E}$ and [/itex]\vec{H}[/itex]. That's why you define the permitivity $\epsilon$ and permeability $\mu$ (for a homogeneous isotropic medium and working in Heaviside-Lorentz units, i.e., $\epsilon$ and [/itex]\mu[/itex] are dimensionless constants and unity in a vacuum) for a medium at rest as
$$\vec{D}=\epsilon \vec{E}, \quad \vec{H}=\frac{1}{\mu} \vec{B}.$$
Now the homogeneous Maxwell equations read
$$\vec{\nabla} \times \vec{E} + \frac{1}{c} \partial_t \vec{B}=0, \quad \vec{\nabla} \cdot \vec{B}=0,$$
and the inhomogeneous ones
$$\vec{\nabla} \times \vec{H} -\frac{1}{c} \partial_t \vec{D}=\frac{1}{c} \vec{j}, \quad \vec{\nabla} \cdot \vec{D}=\rho,$$
where $\vec{j}$ and $\vec{\rho}$ are the free electric current and charge densities, i.e., the currents and charges added to the ones constituting the medium.

If you now insert the consititutive relations, you can derive the wave equations for $\vec{E}$ and [/itex]\vec{B}[/itex], and then you'll get the Helmholtz equation when using the Fourier ansatz
$$\vec{E}(t,\vec{x})=\tilde{\vec{E}}(\vec{x}) \exp(-\mathrm{i} \omega t)$$
and analogous for all the other field quantities as well. Note that (neglecting spatial dispersion) the permitivity and permeablity are functions of $\omega$.