Can you create a standing electromagnetic wave without generating an electric field? I know it is possible to create a "standing" electromagnetic wave by generating it in a space that is limited in size relative to the wave's wavelength in some way. Is there any way of cancelling out the electric field component across the entire wave without also cancelling the magnetic field? Thus maintaining some energy within the space?
 A: If I understand correctly, you want a standing magnetic wave of the form (e.g.)
$$\vec{B} = B_0 \sin (kz) \sin(\omega t)\hat{j}$$
without an electric field?
The problem is that
Maxwell's equations imply the co-existence of a curling electric field with a changing magnetic field, and vice-versa at every point in space.
Since the magnetic field has a non-zero curl and time-derivative, it isn't possible to zero the E-field whilst having a wave-like B-field.
A: To generate an EM wave, one needs synchronous accelerations of electrons in a conductor. The surface electrons then emit photons. Unlike thermal radiation, these photons are polarised. During each half-wave period, their electric components (and their magnetic field components 90° to the electric field) are oriented in the same direction. With the right tuning of the reflecting walls, a standing wave can be obtained.
It is important to understand that in the standing wave photons still fly to the left and after reflection again to the right. Whenever you bring a coupling element into "contact" with the standing wave, or the electric, or the magnetic field component induce a current of electrons in the conductor. This current is driven only through the absorption of photons from the wave. To take away one of the components of an EM wave is impossible. The photon exists from emission to absorption only as an indivisible particle.
There is a tendency to deny the existence of photons.
Ignoring EM radiation to be a stream of photons may be good for mathematical reasons. More illustrative, on the other hand, is the tracking of the behaviour of the photons generated. It quickly becomes clear that photons also move back and forth (to the left and to the right) in the nodes of the standing wave, only their field components (electrical or magnetic) are oriented in opposite directions. In the node, photons can also couple to a medium, but they are immediately re-emitted. At the point of the wave crest, on the other hand, the surface electrons of the medium are moved synchronously (by the absorption of the polarised) photons. A current is created. But only through the loss of photons (as a whole).
