For numerical algorithms and to get a more low level understanding of the equations, we can expand all terms to the simpler and more explicit form:

\frac{\partial E _{x}}{\partial x} + \frac{\partial E _{y}}{\partial x} + \frac{\partial E _{z}}{\partial x} = \frac{ρ}{ε _{0}} \frac{\partial B _{x}}{\partial x} + \frac{\partial B _{y}}{\partial x} + \frac{\partial B _{z}}{\partial x} = 0 \frac{\partial E _{z}}{\partial y} - \frac{\partial E _{y}}{\partial z} = - \frac{\partial B _{x}}{\partial t} \frac{\partial E _{x}}{\partial z} - \frac{\partial E _{z}}{\partial x} = - \frac{\partial B _{y}}{\partial t} \frac{\partial E _{y}}{\partial x} - \frac{\partial E _{x}}{\partial y} = - \frac{\partial B _{z}}{\partial t} \frac{\partial B _{z}}{\partial y} - \frac{\partial B _{y}}{\partial z} = μ_{0} (J_{x} + ε_{0} \frac{\partial E _{x}}{\partial t}) \frac{\partial B _{x}}{\partial z} - \frac{\partial B _{z}}{\partial x} = μ_{0} (J_{y} + ε_{0} \frac{\partial E _{y}}{\partial t}) \frac{\partial B _{y}}{\partial x} - \frac{\partial B _{x}}{\partial y} = μ_{0} (J_{z} + ε_{0} \frac{\partial E _{z}}{\partial t})

Ancestors

Explicit scalar form of the Maxwell's equations