I'm taking E & M II this semester, and one question got me thinking. We know the formulation of the four Maxwell's equations, that's okay so far. But in the absence of sources, they take the form:

$$\nabla \cdot \mathbf{E}= 0 \\ \nabla \cdot \mathbf{B}= 0 \\ \nabla \times \mathbf{E} = -\dfrac{\partial\mathbf{B}}{\partial t}\\ \nabla \times \mathbf{B} = \mu_{0}\epsilon_{0}\dfrac{\partial\mathbf{E}}{\partial t}$$

So my question is, the electric field is caused by the presence of charged particles, which if it varies, causes the existence of a magnetic field. But if there are no sources, how can the Maxwell's equations have nontrivial solutions? Wouldn't the electric and magnetic field be always zero?

I'm taking E & M II this semester, and one question got me thinking. We know the formulation of the four Maxwell's equations, and that's okay so far. But in the absence of sources, they take the form:

$$\nabla \cdot \mathbf{E}= 0 \\ \nabla \cdot \mathbf{B}= 0 \\ \nabla \times \mathbf{E} = -\dfrac{\partial\mathbf{B}}{\partial t}\\ \nabla \times \mathbf{B} = \mu_{0}\epsilon_{0}\dfrac{\partial\mathbf{E}}{\partial t}$$

The electric field is caused by the presence of charged particles, which if it varies, causes the existence of a magnetic field. But if there aren't any sources, how can the Maxwell's equations have nontrivial solutions? Wouldn't the electric and magnetic field always be zero?

I'm taking E&M II this semester and one question got me thinking. I can't thing it on Griffiths or any related questions to this topic, the question is this:

We know the formulation of the four Maxwell's equations, that's okay so far. But in the absence of sources, they take the form:

$$\nabla \cdot \mathbf{E}= 0 \\ \nabla \cdot \mathbf{B}= 0 \\ \nabla \times \mathbf{E} = -\dfrac{\partial\mathbf{B}}{\partial t}\\ \nabla \times \mathbf{B} = \mu\epsilon\dfrac{\partial\mathbf{E}}{\partial t}$$

So my question is, electric field is caused by the presence of charged particles, which if varies, causes the existence of a magnetic field. But if there are no sources, how can the Maxwell's equations have nontrivial solutions? Wouldn't the electric and magnetic field be always zero?

I'm taking E & M II this semester, and one question got me thinking. We know the formulation of the four Maxwell's equations, that's okay so far. But in the absence of sources, they take the form:

$$\nabla \cdot \mathbf{E}= 0 \\ \nabla \cdot \mathbf{B}= 0 \\ \nabla \times \mathbf{E} = -\dfrac{\partial\mathbf{B}}{\partial t}\\ \nabla \times \mathbf{B} = \mu_{0}\epsilon_{0}\dfrac{\partial\mathbf{E}}{\partial t}$$

So my question is, the electric field is caused by the presence of charged particles, which if it varies, causes the existence of a magnetic field. But if there are no sources, how can the Maxwell's equations have nontrivial solutions? Wouldn't the electric and magnetic field be always zero?