Maxwell equations, curl problem

[marcius]

The differiantial form of faraday's law tells that at a any point in space changing with time magnetic field creates the rotor of electric field (let's say circular electric field at that point), but in the centre of the circular field there is no E vector, it's zero, there only is it's rotor that's not zero, so how can both electric and magnetic fields be created at the same point in space (that tells wave equation solution Esin(wt + kx) and Bsin(wt + kx) if varying one field in time at some point of space there is created only the curl of vector field, but not the vector itself? Meanwhile wave equation solutions' graphs are telling that both electric and magnetic fied exist at the same point in space.

 

[Vailanor]

The answer to your question lies in the fact that, while the electric and magnetic fields created by a changing magnetic field are indeed related by curl equations, they are not the same fields. The electric field is a vector field, while the magnetic field is a vector field with a vector potential component. This means that, while they both exist at the same point in space, they are still distinct fields with different properties.The wave equation solution of Esin(wt + kx) and Bsin(wt + kx) is just a way of describing how the electric and magnetic fields interact with each other over time. The wave equation does not actually describe the electric and magnetic fields directly, but rather the relationship between them. In other words, it is a mathematical representation of how the electric and magnetic fields interact with each other.