# Formula Wave equation for B-field

## Magnetic field

Unit
Solving the vectorial wave equation with the respective boundary conditions yields the magnetic field. For example, a simple solution of the wave equation yields the B-field in the form of plane waves.

## Electric field constant

Unit
It is a natural constant and has the value $$\varepsilon_0 = 8.854 \cdot 10^{-12} \, \frac{\text{As}}{\text{Vm}}$$.

## Magnetic field constant

Unit
It is a natural constant and occurs whenever electromagnetic fields are involved. It has the value $$\mu_0 = 4\pi \cdot 10^{-7} \, \frac{ \text{N} }{ \text{A}^2 }$$.

## Nabla operator

Unit
The operator $$\nabla^2$$ is applied to the magnetic field to differentiate the components of the B-field according to the spatial coordinates $$x,y,z$$.

Applying $$\nabla^2$$ to the B-field yields a vector quantity. The first component of this vector quantity is:$\frac{\partial^2 B_x}{\partial x^2} + \frac{\partial^2 B_x}{\partial y^2} + \frac{\partial^2 B_x}{\partial z^2} ~=~ \mu_0 \, \varepsilon_0 \, \frac{\partial^2 B_x}{\partial t^2}$