# Electromagnetic Considerations

• H. F. Tiersten

## Abstract

Maxwell’s equations in Gaussian units are (9)
$$\nabla \times H = \frac{1}{c}\frac{{\partial D}}{{\partial t}} + \frac{{4\pi }}{c}J$$
(4.1)
$$\nabla \times E = - \frac{1}{c}\frac{{\partial B}}{{\partial t}}$$
(4.2)
where H is the magnetic field intensity, E is the electric field intensity, D is the electric displacement vector, and B is the magnetic flux vector. These vector fields are related by the equations
$$D = E + 4\pi P$$
(4.3)
$$B = H + 4\pi M$$
(4.4)
where P is the polarization vector and M is the magnetization vector, with D, E, and P polar vectors, while B, H, and M are axial vectors. Along with the six Maxwell equations, (4.1) and (4.2), we have the auxiliary equations
$$\nabla \cdot B = 0$$
(4.5)
$$\nabla \cdot D = 4\pi {\rho _e}$$
(4.6)
Equation (4.5) is satisfied automatically, and (4.6) simply defines ϱ e such that the equation of the conservation of electric charge
$$\partial {\rho _e}/\partial t + \nabla \cdot J = 0$$
(4.7)
is satisfied.