# Maxwell's Equations and Path of light & Gravitational wave

1. Oct 24, 2008

### spidey

Maxwell's Equations say about the velocity of electromagnetic wave..Does Maxwell's equations also say about path of the electromagnetic wave i.e. light?
I want to know how to find the path of light from Maxwell's equations? Or it says only about velocity?

One more question, what is the path of gravitational wave? is it also the path with shortest time as like light? if light is affected by gravity then,intuitively,gravitational wave should also be affected by electric and magnetic fields? isn't it? what does Maxwell say about this?

2. Oct 25, 2008

### Staff: Mentor

Yes, Maxwell's equations completely describe EM.

The Einstein field equation's stress-energy tensor includes terms for energy density and flux, which would include energy in EM fields. Obviously Maxwell doesn't say anything about this since Einstein developed it quite a while after Maxwell's death.

3. Oct 25, 2008

### rbj

one other thing, is that there are some guys (Mashoon is one name i remember) did some seminal papers in GravitoElectroMagnetism (GEM) . another named Clark did another paper. with differences in scaling (that was absorbed by the Lorentz force equation), they both came up with something that looked like Maxwell's equations given the assumption of reasonably flat space-time. but instead of charge (or charge density) these GEM equations had mass (or mass density) in them. although these guys derived the GEM equations out of the Einstein tensor equation (with the assumption of reasonably flat space-time and speeds much less than c), i've always felt that such corresponding equations to E&M were to be expected since both actions were inverse-square and both actions were believed to propagate at the same finite speed of c.

$$\nabla \cdot \mathbf{E} = -4 \pi G \rho \$$

$$\nabla \cdot \left( \frac{1}{2} \mathbf{B} \right) = 0 \$$

$$\nabla \times \mathbf{E} = -\frac{1}{c} \frac{\partial \left( \frac{1}{2} \mathbf{B} \right)} {\partial t} \$$

$$\nabla \times \left( \frac{1}{2} \mathbf{B} \right) = \frac{1}{c} \left( -4 \pi G \mathbf{J} + \frac{\partial \mathbf{E}} {\partial t} \right) = \frac{1}{c} \left( -4 \pi G \rho \mathbf{v}_{\rho} + \frac{\partial \mathbf{E}} {\partial t} \right) \$$

For a test particle of small mass, m, the net (Lorentz) force acting on it due to GEM fields is:

$$\mathbf{F}_{m} = m \left( \mathbf{E} + \frac{1}{c} \mathbf{v}_{m} \times \mathbf{B} \right)$$

if you eliminate $\mu_0$ (by substituting $1/(\epsilon_0 c^2))$ and replace $1/(4 \pi \epsilon_0)$ with -G (the minus sign because, although like-signed electric charges repel, like-signed masses attract each other) and charge density with mass density, you get the above GEM equations except for a pesky factor of 1/2 which i am told is due to the fact that gravitation is some kinda "spin 2" field while E&M is a "spin 1". i dunno what that's all about, so i am just reverberating the terms.

but if you want to quantitative describe the propagation of gravity waves, i think the GEM equations are s'posed to be pretty accurate.

Last edited: Oct 25, 2008
4. Oct 25, 2008

### spidey

thanks for the info..