Advanced Electromagnetic and Mathematic Concepts

[Michael Lin]

Hi All,

From electromagnetic theories, with the Lorentz gauge condition for the magnetic vector potential, I get the following wave equation:
1/csquared * d2A/dt2 + del2 A= u0 j.
in some literatures, they ignored the d2A/dt2 term and I don't know why they can do that. Is it becasue they assumed some quasi-stationary condition on the E field created by the magnetic field?
This simplication leads to a big simplification in which they can solve it as a Poisson Equation. I just want to know why they can ignore that term.

Thanks,
Micahel

 

[Physics Monkey]

Yes, it is typically called the quasistatic approximation. You keep the Faraday term $$\partial B/ \partial t$$ in Maxwell's equations, but drop the Maxwell term $$\partial E/ \partial t$$. This is an approximation which is valid in some limited circumstances where the displacement current (Maxwell term) is small compared to the real current. A typical scenario might be a wire loop in a magnetic field and the like.

More properly, by leaving out the Maxwell term you ignore the possibility of electromagnetic waves. To justify this approximation, the frequencies of interest in your system must correspond to electromagnetic waves of wavelength much larger than your system of interest. In other words, everything should be slowly varying or "quasistatic".