- #1
Gregg
- 459
- 0
In lectures we have been given:
## \vec{\nabla} \cdot \vec{D} = \rho_{\text{free}} ##
## \vec{\nabla} \times \vec{H} = \vec{J}_{\text{free}} + \frac{\partial \vec{D}}{\partial t} ##
## \vec{\nabla} \times \vec{E} = - \frac{\partial \vec{B}}{\partial t} ##
## \vec{\nabla} \cdot \vec{B} = \vec{0} ##
I need examples to work out why ##\vec{D}## and ##\vec{H}## are such a convenience for me. This is something I can't see at all!
## \vec{D} = \epsilon_r \epsilon_0 \vec{E} ## ? So it should be useful in dielectrics, and ## \vec{D} = \epsilon_0 \vec{E} + \vec{P} ## so polarisation is defined as the E field caused by a relative dielectric constant in some dielectric material?
The there's ## \vec{H} = \frac{\vec{B}}{\mu_0} - \vec{M} ## and also I guess ## \frac{\vec{B}}{\mu_0 \mu_r} = \vec{H}## ? So the magnetisation is the magnetic field due to some medium with relative permeability?
But why are these vector fields useful for calculations?
## \vec{\nabla} \cdot \vec{D} = \rho_{\text{free}} ##
## \vec{\nabla} \times \vec{H} = \vec{J}_{\text{free}} + \frac{\partial \vec{D}}{\partial t} ##
## \vec{\nabla} \times \vec{E} = - \frac{\partial \vec{B}}{\partial t} ##
## \vec{\nabla} \cdot \vec{B} = \vec{0} ##
I need examples to work out why ##\vec{D}## and ##\vec{H}## are such a convenience for me. This is something I can't see at all!
## \vec{D} = \epsilon_r \epsilon_0 \vec{E} ## ? So it should be useful in dielectrics, and ## \vec{D} = \epsilon_0 \vec{E} + \vec{P} ## so polarisation is defined as the E field caused by a relative dielectric constant in some dielectric material?
The there's ## \vec{H} = \frac{\vec{B}}{\mu_0} - \vec{M} ## and also I guess ## \frac{\vec{B}}{\mu_0 \mu_r} = \vec{H}## ? So the magnetisation is the magnetic field due to some medium with relative permeability?
But why are these vector fields useful for calculations?